Assuming the ball follows a parabolic path: Find the time it takes the ball to h

Question

Assuming the ball follows a parabolic path: Find the time it takes the ball to hit the ground. How far in the horizontal direction has the ball traveled? Find the x and y component of the velocity' when the ball strikes the ground. Write it in vector form. A 30.0 kg block lying on a horizontal surface is connected to a 60kg block by a cord that passes over a pulley. The 60 kg block is hanging. The pulley is frictionless and of negligible mass. Neglect the mass of the string. The coefficient of kinetic friction between the 30.0 kg block and the surface is mu_k = 0.20. Find the acceleration of the system. Find the tension in the cord. Find the distance the 60 kg mass descends 3 seconds after release.

Explanation / Answer

The net force F=ma on the 60kg block is Fg-T

so F=ma=Fg-T

ma=mg-T

60a=60g-T

For the 30kg block, F=ma= T-Ff

ma= T -miew *mg

30a= T-0.2 * 30*g

isolate for T in first equation : 60a=60g-T so T= 60g-60a

in second equation :   30a= T-0.2 * 30*g so T= 30a +0.2*30g

set T equal: 60g-60a= 30a +0.2*30g

solve for a 529.2= 90a   

a= 5.88 m/s^2

PART B

plug a into T= 60g-60a = 60*9.8-60*5.88=235.2 N

PART C

we know that t= 3, a= 5.88, v1 =0 , find d

d= v1 *t +1/2 *at*2

d= 1/2 *5.88*3^2 = 26.46 m

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