. A person kicks a rock off a cliff horizontally with a speed of 20 m/s. It takes 7.0 seconds to hit the ground, find:
a) height of the cliff
b) final vertical velocity
c) range
To find the height of the cliff, we can use the formula for vertical motion:
1. Use the equation h = ut + (1/2)gt², where:
- h is the height of the cliff
- u is the initial vertical velocity (0 m/s since the rock was kicked horizontally)
- t is the time taken for the rock to hit the ground (7.0 s)
- g is the acceleration due to gravity (-9.8 m/s²)
Substituting the values, we have:
h = (0)(7.0) + (1/2)(-9.8)(7.0)²
Calculating this equation gives us the height of the cliff.
To find the final vertical velocity, we can use the formula:
2. vf = u + gt, where:
- vf is the final vertical velocity
- u is the initial vertical velocity (0 m/s)
- g is the acceleration due to gravity (-9.8 m/s²)
- t is the time taken for the rock to hit the ground (7.0 s)
Substituting the values, we have:
vf = 0 + (-9.8)(7.0)
Calculating this equation gives us the final vertical velocity.
To find the range, we can use the formula for horizontal motion:
3. R = vxt, where:
- R is the range
- vx is the horizontal velocity (20 m/s)
- t is the time taken for the rock to hit the ground (7.0 s)
Substituting the values, we have:
R = (20)(7.0)
Calculating this equation gives us the range.
To answer these questions, we can use the principles of projectile motion. First, let's break down the given information:
Initial velocity in the horizontal direction (ux) = 20 m/s
Time of flight (t) = 7.0 seconds
a) Height of the cliff:
Since the rock was kicked horizontally, the initial vertical velocity (uy) is 0 m/s. We can use the formula for vertical displacement in projectile motion:
h = (uy * t) + (0.5 * g * t^2)
Since uy = 0, the equation simplifies to:
h = 0.5 * g * t^2
where g is the acceleration due to gravity. Taking g as approximately 9.8 m/s^2:
h = 0.5 * (9.8 m/s^2) * (7.0 s)^2
h = 0.5 * 9.8 m/s^2 * 49 s^2
h = 240.1 m
Therefore, the height of the cliff is approximately 240.1 meters.
b) Final vertical velocity:
The final vertical velocity (vf) can be determined using the equation:
vf = uy + (g * t)
Since the initial vertical velocity, uy, is 0 m/s:
vf = 0 + (9.8 m/s^2 * 7.0 s)
vf = 68.6 m/s
Therefore, the final vertical velocity is 68.6 m/s.
c) Range:
Since the initial horizontal velocity (ux) remains constant throughout the motion, the range (R) can be calculated using the equation:
R = ux * t
R = (20 m/s) * (7.0 s)
R = 140 m
Therefore, the range is 140 meters.
height: s = 4.9t^2
speed: 9.8t
range: 20t