Question

A ball is thrown horizontally from 20 m high building with a speed of 5.0 m/s.

(a) Make a sketch of the ball’s trajectory.

(b) Draw a graph of Vx, the vertical velocity, as a funtion of time.

(c) Draw a graph of Vy, the vertical velocity, as a funtion of time.

(d) How far from the base of the building does the ball hit the ground?

Answer 1

a)

Given ball is thrown horizontally with speed of 20 m/s

Horizontal velociy will remain constant and vertical velocity will keep increasing due to acceleration due to gravity

Let the origin be at the point from where the ball is thrown

Let x axis be towards right in the same direction as the ball is thrown. Also, let y axis point vertically downwards

At any time t, x coordinate is given by ,x=20t

At any time t, y coordinate is given by y=0.5*9.8*t²=4.9t²

Substituting t=x/20 ww get

y=4.9*(x/20)²=0.01225x²

Therefore the trajectory can be plotted with the above equation

b) since there is no horizontal acceleration, horizontal velociyy wiill be constant and equal to 20 m/s at any given time

c)initial vertical velocity=0

Acceleration in vertical direction=acceleration due to gravity=9.8 m/s²

Vertical velocity=0+(9.8t)=9.8t

Therefore plot ofvertical.velocitu with time is a line with slope of 9.8 and passi g through the origin

d)let time taken by ball to reach ground be t

20=0.5*9.8*t²

t=2.86 seconds

Horizontal distance travelled by ball in that time=20*2.86=57.14 m

Therefore, the ball hits the ground 57.14 m from the base of building