35. l A sprinkler mounted on the ground sends out a jet of water at a 30° angle

Question

35. l A sprinkler mounted on the ground sends out a jet of water at a 30° angle to the horizontal. The water leaves the nozzle speed of 12 m/s. How far does the water travel before it hits the ground? at a 36. l A good quarterback can throw a football at 27 m/s (about 60 mph). If we assume that the ball is caught at the same height from which it is thrown, and if we ignore air resistance, what is the maximum range in meters (which is approximately the same as the range in yards) of a pass at this speed? How long is the ball in the air?

Explanation / Answer

Given,

theta = 30 deg ; v0 = 12 m/s

Let D be the required distance.

This motion of water stream can be modelled as the motion of a projectile. So,

The vertical and horizontal component of velocity will be:

vx = 12 x cos30 = 10.39 m/s

vy = 12 x sin30 = 6 m/s

time taken to reach maximum height will be:

t = vy/g = 6/9.8 = 0.61

time of flight will be:

T = 2t = 1.22 s

Range/horizontal distance will be:

D = vx T = 10.39 x 1.22 = 12.68 m

Hence, D = 12.68 m

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