I have 2 different types of physic questions. questions are long but answers sho

Question

I have 2 different types of physic questions. questions are long but answers should be ez but i dont get them

A balloon is rising with a constant velocity of vballoon = 84.65-m/s. A ball is dropped from the balloon when it is at a height of h = 56.5-m. What is the magnitude of the initial velocity for the ball? Assume that down is positive.

answer : __________m/s

What is the final velocity of the ball when it reaches the ground? ________m/s

How long does the ball take to reach the ground? ________s

Also,

A car travels north with a velocity of 3.5-m/s for 29-seconds. It then turns east, and with the same speed travels for a further 23-seconds. Calculate the magnitude of the final displacement of the car.

answer : _____________m

Now give the direction of the final displacement of the car. Give your answer in degrees North of East.

answer : ___________ degrees

Explanation / Answer

Since ball is in the balloon it will have same velocity as balloon = 84.65 m/s

Thus vi = 84.65 m/s

Now final velocity,

vf^2 = vi^2 + 2ah

vf^2 = 84.65^2 + (2*-9.8*-56.5)

Gives, vf = - 91.0 m/s….minus since downward

Now time,

vf= vi – gt

- 91.0 = 84.65 – 9.8*t

Gives, t= 17.9s

d1= v1*t1 = (3.5*29.0) = 101.5 m

d2 = v2*t2 = (3.5*23.0) = 80.5 m

D=sqrt( d1^2 + d2^2) = sqrt(101.5^2 + 80.5^2) = 129.55 m

= tan^1(d2/d1)= tan^-1(80.5/101.5) = 38.42 deg

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