1. What is the speed of a 70kg rock after it has fallen freely for 1000m?
2. How far would a 1kg ball have to fall freely to reach a speed of 100km/h?
To answer these questions, we can make use of the principles of physics, specifically those related to free-fall motion. The equations we need are derived from the laws of motion and gravity.
1. What is the speed of a 70kg rock after it has fallen freely for 1000m?
To determine the speed, we need to find the final velocity of the rock. We can use the formula for free-fall velocity:
v = sqrt(2gh)
where:
- v is the final velocity,
- g is the acceleration due to gravity (approximately 9.8 m/s²),
- h is the height or distance fallen.
Let's calculate it step-by-step:
1. Determine the acceleration due to gravity (g) - 9.8 m/s².
2. Determine the height fallen (h) - 1000m.
3. Plug the values into the formula: v = sqrt(2 * 9.8 * 1000).
4. Calculate the result: v ≈ 44.2 m/s.
Therefore, the speed of the 70kg rock after it has fallen freely for 1000m is approximately 44.2 m/s.
2. How far would a 1kg ball have to fall freely to reach a speed of 100km/h?
In this case, we need to find the height or distance fallen (h). To solve for h, we rearrange the velocity formula:
h = v² / (2g)
where:
- h is the height or distance fallen,
- v is the final velocity,
- g is the acceleration due to gravity (approximately 9.8 m/s²).
Let's calculate it step-by-step:
1. Convert the final velocity from km/h to m/s: 100 km/h = (100 * 1000) / 3600 ≈ 27.8 m/s.
2. Determine the acceleration due to gravity (g) - 9.8 m/s².
3. Plug the values into the formula: h = (27.8)^2 / (2 * 9.8).
4. Calculate the result: h ≈ 39.8 meters.
Therefore, a 1kg ball would need to fall freely for approximately 39.8 meters to reach a speed of 100 km/h.
1. vf^2=vi^2+2g*d
vi is zero, solve for vf
2. change km/hr to m/s
same formula. Mass is not needed.