Question

as shown in the diagram below, a student standing on the roof of a 50.0 meter high building kicks a stone at a horizontal speed of 4.00 meters per second. How much time is required for the stone to reach the level ground below?

Answer 1

The time required for a stone to reach the ground after being kicked horizontally from a 50-meter-high building is approximately 3.19 seconds, calculated using the equation of motion under constant acceleration due to gravity.

Step-by-step explanation:

The question asks about the time a stone takes to hit the ground if kicked horizontally from the roof of a 50.0 meter high building. To determine the time required for the stone to reach the level ground, we use the formula for the time of flight for an object under the influence of gravity alone (since horizontal velocity does not affect the time taken to fall vertically). The formula derived from the equations of motion under constant acceleration is t = √(2h/g), where h is the initial height (50.0 meters) and g is the acceleration due to gravity (9.81 m/s²). Plugging in the values, we get t = √(2 * 50.0 / 9.81) ≈ 3.19 seconds, which is the time required for the stone to reach the ground.

Answer 2

We can use the kinematic equation for vertical motion:

y = v0*t + (1/2)at^2

where y is the height, v0 is the initial velocity (in the vertical direction), a is the acceleration (due to gravity), and t is the time.

At the highest point of the stone's trajectory, its vertical velocity will be zero, so we can use the initial velocity as 0 and the acceleration as -9.8 m/s^2.

Using the height of the building as the initial height, we get:

-50.0 m = 0*t + (1/2)(-9.8 m/s^2)*t^2

Simplifying and solving for t, we get:

t = sqrt(2*(-50.0 m) / -9.8 m/s^2) = 3.19 seconds

Therefore, it will take approximately 3.19 seconds for the stone to reach the level ground below. Note that the horizontal speed of the stone does not affect the time it takes to fall vertically.