Problem 1 (2D Kinematics) ball is thrown straight upward and returns to the thro

Question

Problem 1 (2D Kinematics) ball is thrown straight upward and returns to the thrower's hand after 3.00 s in the air. A second ball is thrown at an angle of 30.0° with the horizontal. At what speed must the second ball be thrown so that it reaches the same height as the one thrown vertically? Problem 2 (Newton's Second Law) A boat moves through the water with two forces acting on it. One is a 2 000-N forward push by the water on the pro- peller, and the other is a 1 800-N resistive force due to the water around the bow. (a) What is the acceleration of the 1000-kg boat? (b) If it starts from rest, how far will the boat move in 10.0 s? (c) What will its velocity be at the end of that time? Problem 3 (Statics (a) Find the tension in 87 each cable supporting the 600-N cat burglar (b) Suppose the hori- zontal cable were reattached higher up on the wall. Would 600 N the tension in the other cable increase, decrease, or stay the same? Why?

Explanation / Answer

1.

1.

In case1 when ball is thrown vertically upward

given time taken = 3.0 sec

time to reach max height = total time/2 = 3/2 = 1.5 sec

Suppose initial velocity is = Vi

then using equation

Vf = Vi + a*t

Vf = speed at max height = 0 m/sec

0 = Vi - 9.8*1.5

Vi = 9.8*1.5 = 14.7 m/sec

Now max height will be

Vf^2 = Vi^2 + 2*a*h

h = (0^2 - 14.7^2)/(2*(-9.8)) = 11.03 m

Now in case 2:

In projectile motion max height is given by:

Hmax = V0^2*(sin theta)^2/2g

V0 = sqrt (Hmax*2*g/(sin theta)^2)

V0 = sqrt (11.03*2*9.81/(sin 30 deg)^2)

V0 = 29.42 m/sec

So second ball must be thrown at 29.42 m/sec

2.

Using net force balance on Boat

Fnet = Fp - Fr

Fp = forward push force = 2000 N

Fr = resistive force = 1800 N

Fnet = m*a

m*a = Fp - Fr

a = (Fp - Fr)/m

a = (2000 - 1800)/1000 = 0.2 m/sec^2

Part B

Using equation

d = U*t + 0.5*a*T^2

U = 0 = initial speed

t = 10 sec

a = 0.2m/sec^2

So,

d = 0*10 + 0.5*0.2*10^2

d = 10 m

Part C

V = U + a*t

V = 0 + 0.2*10

V = 2 m/sec

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