A ball with mass 0.15kg is thrown upwardswith initial velocity 20 m/sec from the roof of a building 30mhigh. There is a force due to air resistance of v^2 / 1325 .where the velocity is measured in m/sec. (a) Find max height above ground ball reaches. (b) Find the time that the ball hits the ground.

wendi1019gt

wendi1019gt

Answered question

2022-08-04

A ball with mass 0.15kg is thrown upwardswith initial velocity 20 m/sec from the roof of a building 30mhigh. There is a force due to air resistance of v 2 / 1325.where the velocity is measured in m/sec.
(a) Find max height above ground ball reaches.
(b) Find the time that the ball hits the ground.

Answer & Explanation

Favatc6

Favatc6

Beginner2022-08-05Added 17 answers

First the model: F = m a = m g v 2 / 1325. We find d v d t = g v 2 198.75 = g v 2 c
c=198.75.
This is a separable equation:
d v g + v 2 c = d t d v 1 + v 2 g c = g d t and integrate left and right:
c g tan 1 ( v c g ) = g t + K 1
and we find tan 1 ( v c g ) = g c t + K 2 which means v c g = tan ( g c t + K 2 ) and we find v ( t ) = tan ( g c t + K 2 ) c g
and you can determine x(t) by integration (anti derivative of tan ( x )   i s   ln ( cos ( x ) )).
and the initial condition v(0)=20, x(0)=30.

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