Question

Problem 6:

A hose lying on the ground shoots a stream of water upward at an angle of 40° to the horizontal. The speed of the water is 20 m/s as it leaves the house. How high up will it strike a wall which is 8 m away?

Answer 1

Answer 2

SOLUTION :

Hose at ground level shoots water at an angle of 40º and speed of 20 m/s. 

So, 

horizontal speed  of water, Vh = 20 cos (40º) = 15.32 m/s

vertical speed  of water , Vv = 20 sin (40º) = 12.85575 m/s

Wall is 8m away.

Time needed to reach the wall 

= Distance / Horizontal Speed 

= 8 / 15.32

= 0.5222 sec.

In the vertical direction gravity will decelerate the vertical speed 

at the deceleration rate of 9.8 m/sec^2 .

So, 

Height achieved in t secs. = u t - 1/2 g t^2 

So, height achieved in 0.522 secs. 

= (12.85575)(0.5222) - 1/2 * 9.8 * (0.5222)^2

= 5.377  = 5.38 meters.

Hence, water will hit the 8 meter away wall at a height of 5.38 m approx.

(ANSWER)