A hockey player hits the ball that gives a velocity of 32 m/s at angle 20° form with the horizontal. Calculate the following:
A. What is the component of the initial velocity
B. What is the maximum height
C. Time to reach the maximum height
D. What is the range
What is the component of the initial velocity?
The initial velocity is 32 m/s and has two components, one horizontal and one vertical.
Horizontal component, Vh = V.cos(α) = 32.cos(20) = 30.07
Vh = 30 m/s
Vertical component, Vv = V.sin(α) = 32.sin(20) = 10.94
Vv = 10.94 m/s
What is the maximum height?
Using v^2 – u^2 = 2as
0 – Vv^2 = -2gh
h = Vv^2/2g = 10.94^2/19.6 = 6.1
Max height, h = 6.1 m
Time to reach the maximum height
Using v = u + at
0 = Vv – gt
t = Vv/g = 10.94/9.8 = 1.116
Time to reach the maximum height is t = 1.116 s
What is the range?
Flight time T = 2*1.116 = 2.232 s
Horizontal velocity is Vh = 30 m/s
Range = Vh*t = 30*2.232 = 66.96
Range = 67 m