Free Fall worksheet

1. Time to hit the ground: 3.89 s

1. Use the surface gravity of Mars

   $g$$=3.71\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 3.71\times 28}$$=14.413882\text{\hspace{0.17em}m/s}$

3. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 28}{0+14.413882}$$=3.885143\text{\hspace{0.17em}s}$

4. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 3.71\times 1^2$$=1.855\text{\hspace{0.17em}m}$

5. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+3.71\times 1$$=3.71\text{\hspace{0.17em}m/s}$

2. Time to hit the ground: 4.3 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 15}$$=6.97137\text{\hspace{0.17em}m/s}$

3. Change the answer to km/h, the unit you picked: divide by 0.277777777778

   $\frac{6.97137}{0.277777777778}$$=25.096932\text{\hspace{0.17em}km/h}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 15}{0+6.97137}$$=4.303315\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 1.62\times 1^2$$=0.81\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 1$$=1.62\text{\hspace{0.17em}m/s}$

3. Time to hit the ground: 4.71 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 18}$$=7.636753\text{\hspace{0.17em}m/s}$

3. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 18}{0+7.636753}$$=4.714045\text{\hspace{0.17em}s}$

4. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 1.62\times 1^2$$=0.81\text{\hspace{0.17em}m}$

5. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 1$$=1.62\text{\hspace{0.17em}m/s}$

4. Time to hit the ground: 2.38 s

1. Use the gravity value you entered

   $g$$=8.5\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 8.5\times 24}$$=20.19901\text{\hspace{0.17em}m/s}$

3. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 24}{0+20.19901}$$=2.376354\text{\hspace{0.17em}s}$

4. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 8.5\times 1^2$$=4.25\text{\hspace{0.17em}m}$

5. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+8.5\times 1$$=8.5\text{\hspace{0.17em}m/s}$

5. Time to hit the ground: 2.94 s

1. Use the surface gravity of Mars

   $g$$=3.71\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 3.71\times 16}$$=10.895871\text{\hspace{0.17em}m/s}$

3. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 16}{0+10.895871}$$=2.936892\text{\hspace{0.17em}s}$

4. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 2+0.5\times 3.71\times 2^2$$=7.42\text{\hspace{0.17em}m}$

5. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+3.71\times 2$$=7.42\text{\hspace{0.17em}m/s}$

6. Time to hit the ground: 5.88 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 28}$$=9.524705\text{\hspace{0.17em}m/s}$

3. Change the answer to mph, the unit you picked: divide by 0.44704

   $\frac{9.524705}{0.44704}$$=21.306158\text{\hspace{0.17em}mph}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 28}{0+9.524705}$$=5.879447\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 2+0.5\times 1.62\times 2^2$$=3.24\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 2$$=3.24\text{\hspace{0.17em}m/s}$

7. Time to hit the ground: 2.17 s

1. Use the gravity value you entered

   $g$$=11\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 11\times 26}$$=23.916521\text{\hspace{0.17em}m/s}$

3. Change the answer to km/h, the unit you picked: divide by 0.277777777778

   $\frac{23.916521}{0.277777777778}$$=86.099477\text{\hspace{0.17em}km/h}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 26}{0+23.916521}$$=2.174229\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 11\times 1^2$$=5.5\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+11\times 1$$=11\text{\hspace{0.17em}m/s}$

8. Time to hit the ground: 5.21 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 22}$$=8.442748\text{\hspace{0.17em}m/s}$

3. Change the answer to km/h, the unit you picked: divide by 0.277777777778

   $\frac{8.442748}{0.277777777778}$$=30.393894\text{\hspace{0.17em}km/h}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 22}{0+8.442748}$$=5.211573\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 2+0.5\times 1.62\times 2^2$$=3.24\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 2$$=3.24\text{\hspace{0.17em}m/s}$

9. Time to hit the ground: 4.71 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 18}$$=7.636753\text{\hspace{0.17em}m/s}$

3. Change the answer to ft/s, the unit you picked: divide by 0.3048

   $\frac{7.636753}{0.3048}$$=25.054965\text{\hspace{0.17em}ft/s}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 18}{0+7.636753}$$=4.714045\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 1.62\times 1^2$$=0.81\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 1$$=1.62\text{\hspace{0.17em}m/s}$

10. Time to hit the ground: 4.71 s

1. Use the surface gravity of the Moon

   $g$$=1.62\text{\hspace{0.17em}m/s²}$

2. Find the landing speed. Gravity adds speed over the whole drop height, so v² = u² + 2gh

   $\sqrt{0^2+2\times 1.62\times 18}$$=7.636753\text{\hspace{0.17em}m/s}$

3. Change the answer to mph, the unit you picked: divide by 0.44704

   $\frac{7.636753}{0.44704}$$=17.08293\text{\hspace{0.17em}mph}$

4. Divide the height by the average speed to get the time. The average speed is halfway between the start and landing speeds

   $\frac{2\times 18}{0+7.636753}$$=4.714045\text{\hspace{0.17em}s}$

5. Find how far it has fallen by your chosen time: d = u × t + ½ × g × t²

   $0\times 1+0.5\times 1.62\times 1^2$$=0.81\text{\hspace{0.17em}m}$

6. Find its speed at that time. Gravity adds g to the speed every second: v = u + g × t

   $0+1.62\times 1$$=1.62\text{\hspace{0.17em}m/s}$