can some one please help me with these 3 questions. thank you in advance A light

Question

can some one please help me with these 3 questions. thank you in advance

A light year is defined as the distance that light travels in one year. If the speed of light is c-3.0 x 10" meters/second, how many miles are there in one light year? 15 points 0-10 m/s , mileS 12 A ball is thrown vertically upward and rises to a height of 20 meters. (a) What was the ball's initial velocity? |2 pointsl (b) How long will the ball be in the air? 13 points) Oa. A jet fighter starts from rest on an aircraft carrier and reaches a speed of 42 meters/seconds in 2 seconds prior to takeof. Assuming the acceleration of the jet was constant throughout this interval, how long is the runway? (5 points)

Explanation / Answer

1)
One light year = c x 1 year in seconds
= 3 x 108 x 365 x 24 x 60 x 60
= 9.46 x 1015 m
One mile = 1.61 x 103 m

Number of miles = [9.46 x 1015] / [1.61 x 103]
= 5.879 x 1012

2)
Take u as the initial velocity.
Final velocity, v = 0         [At the highest point, the ball comes to a stop and then starts to fall down]
Distance traveled, H = 20 m
Acceleration, a = - 9.81 m/s2.

a)
Using the equation, v2 - u2 = 2as,
0 - u2 = 2 x (-9.81) x 20
u2 = 392.4
u = SQRT[392.4]
= 19.81 m/s.

b)
Using the equation, v = u + at
0 = 19.81 + (-9.81) x t
t = 19.81/9.81
= 2.02 s

3)
Initial velocity, u = 0
Final velocity, v = 42 m/s
Time taken, t = 2 s
Acceleration, a = (v - u)/t           [From the equation v = u +at]
= 42/2 = 21 m/s2.

Consider s be the distance traveled.
Using the equation, s = ut + 1/2 at2,
s = 0 + 0.5 x 21 x 4
= 42 m.

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