Question

A student throws a baseball horizontally at 25 m/s from a cliff 45 meters above level ground. approximately how lar from the base of the chft does the bal hit the ground?

Answer 1

To determine the horizontal distance from the base of the cliff where the baseball will hit the ground, we calculate the time of flight using the vertical displacement and acceleration due to gravity. The time is found to be approximately 3.03 seconds, and the horizontal distance traveled is calculated using the horizontal velocity and time, resulting in a distance of approximately 75.75 meters.

Step-by-step explanation:

To determine how far from the base of the cliff the baseball will hit the ground, we need to consider the motion of the ball as two separate components: the horizontal motion at a constant velocity, since there are no horizontal forces acting on it after it is thrown, and the vertical motion, which is affected by gravity.

First, we need to calculate the time it takes for the baseball to hit the ground. For the vertical motion, the initial vertical velocity is 0 m/s, as the ball is thrown horizontally. We'll use the following kinematic equation for uniformly accelerated motion to find the time (t):

• s = ut + 1/2 at^2

Where:
s = vertical displacement (45 m)
u = initial vertical velocity (0 m/s)
a = acceleration due to gravity (9.81 m/s^2)
t = time in seconds

This gives us:

45 m = 0 m/s × t + 1/2 × 9.81 m/s2 × t2

Solving this quadratic equation for t, we find that it takes approximately 3.03 seconds for the baseball to reach the ground.

Now, we'll calculate the horizontal distance (d) using the horizontal velocity (25 m/s) and the time (t) calculated above:

d = v × t

d = 25 m/s × 3.03 s

d = 75.75 m

Therefore, the ball will hit the ground approximately 75.75 meters from the base of the cliff.