A pebble is thrown horizontally from the top of a 25.0 m cliff and hits the ground 11.0 m from the edge of the cliff.
a. How long will it take for the pebble to hit the ground?
b. At what speed the pebble was thrown initially?
c. How much is the horizontal component of the impact velocity?
e. How much is the pebble's impact velocity?
To solve this problem, we can use the kinematic equations to find the answers. The key information we have is the vertical displacement (25.0 m) and the horizontal displacement (11.0 m).
Let's solve each part of the problem step by step:
a. How long will it take for the pebble to hit the ground?
We can use the vertical displacement and the equation of motion:
s = ut + (1/2)gt^2
where:
s = vertical displacement (25.0 m)
u = initial vertical velocity (unknown)
t = time taken (unknown)
g = acceleration due to gravity (9.8 m/s^2)
Since the pebble is thrown horizontally, its initial vertical velocity (u) is 0. Therefore, the equation simplifies to:
25.0 m = 0.5 * 9.8 m/s^2 * t^2
Solving for t:
t^2 = (2 * 25.0 m) / 9.8 m/s^2
t^2 = 5.102 seconds^2
t ≈ √5.102 s
t ≈ 2.26 seconds
Therefore, it will take approximately 2.26 seconds for the pebble to hit the ground.
b. At what speed was the pebble thrown initially?
To determine the speed, we need to find the horizontal component of the pebble's velocity. Since there is no vertical acceleration, the horizontal component of the velocity remains constant.
We can use the equation:
s = ut
where:
s = horizontal displacement (11.0 m)
u = initial horizontal velocity (unknown)
t = time (2.26 s)
Rearranging the equation for u:
u = s / t
u = 11.0 m / 2.26 s
u ≈ 4.87 m/s
Therefore, the pebble was initially thrown with a speed of approximately 4.87 m/s.
c. How much is the horizontal component of the impact velocity?
The horizontal component of the impact velocity is the same as the initial horizontal velocity (u) because there is no horizontal acceleration.
So, the horizontal component of the impact velocity is approximately 4.87 m/s.
d. How much is the pebble's impact velocity?
To determine the pebble's impact velocity, we need to calculate the vertical component of the velocity.
Since the pebble is thrown horizontally, there is no change in the vertical velocity throughout its flight. Therefore, the vertical component of the pebble's velocity at impact is the same as the vertical component of the velocity at the start.
We can use the equation:
v = u + gt
where:
v = final vertical velocity (unknown)
u = initial vertical velocity (0 m/s since it was thrown horizontally)
g = acceleration due to gravity (9.8 m/s^2)
t = time taken (2.26 s)
Plugging in the values:
v = 0 + (9.8 m/s^2 * 2.26 s)
v ≈ 22.1 m/s
Therefore, the pebble's impact velocity is approximately 22.1 m/s.