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?
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)
A hose lying on the ground shoots a stream of water upward at an angle of 40° to the horizontal
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