Calculating the Height and Time of a Kicked Stone

[xplozno8]

Homework Statement

Bill stands on a bridge kicking stones into the water below.

A) If Bill kicks a stone with a horiz velocity of 3.5 m/s and it lands in the water a horiz distance of 5.4 m from where he is standing, what is the height of the bridge?

B) IF the stone had been kicked harder, how would this affect the time it would take to fall?

Homework Equations

The Attempt at a Solution

Don't know how to begin.

 

[Astronuc]

From the horizontal velocity and horizontal distance, one can compute the time traveled.

During the horizontal travel (same time), the stone also falls under the influence of gravity. How far does it fall in that time?


A good reference -

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html


The time of falling is the temporal constraint.

 

[m2003]

I would approach this problem by first identifying the relevant equations and variables. The equations that are relevant to this problem are those related to projectile motion, specifically the equations for horizontal and vertical displacement.

For part A, we can use the equation for horizontal displacement, x = v0t + 1/2at^2, where x is the horizontal displacement, v0 is the initial velocity, t is the time, and a is the acceleration, which in this case is 0 since there is no acceleration in the horizontal direction. We are given the values for x (5.4 m) and v0 (3.5 m/s), so we can rearrange the equation to solve for t. t = x/v0 = 5.4 m / 3.5 m/s = 1.54 seconds.

Next, we can use the equation for vertical displacement, y = v0t + 1/2at^2, where y is the vertical displacement, v0 is the initial velocity, t is the time, and a is the acceleration, which in this case is -9.8 m/s^2 due to gravity. Since the stone is being kicked from the same height as the bridge, the initial vertical displacement is 0. We can solve for t by rearranging the equation: t = sqrt(2y/a) = sqrt(2(0)/-9.8 m/s^2) = 0 seconds.

Therefore, the height of the bridge is 0 meters.

For part B, if the stone was kicked harder, the initial velocity (v0) would increase. This would result in a larger horizontal displacement (x) and a longer time (t) for the stone to reach the water. However, the time for the stone to fall would remain the same, as it is determined by the acceleration due to gravity and the initial vertical displacement (which is still 0 in this case).

In conclusion, by using the equations for projectile motion, we can determine the height of the bridge and understand how increasing the initial velocity affects the time it takes for the stone to reach the water.