Question

The answers to these physics problems are from my textbook. I need help with getting to the answer.

1) an automobile manufacturer claims that its product will, starting from rest, travel 0.40 km in 9.00s. What is the magnitude of the constant acceleration required to do this?

answer: 9.9 m/s^2

2) A stone is thrown from the top of a building with an initial velocity of 20 m/s downward. The top of the building is 60 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground?

answer: 2.0 s

3) An object is thrown downward with an initial t = 0 speed of 10 m/s from a height of 60 m above the ground. At the same instant t = 0, a second object is propelled vertically upward from ground level with a speed of 40 m/s. At what height above the ground will the two objects pass each other?

answer: 41 m

Answer 1

1.

Using 2nd kinematic equation to solve this question

d = U*t + (1/2)*a*t^2

d = distance = 0.40 km = 400 m

U = initial velocity = 0 m/sec

t = time taken = 9.00 sec

a = acceleration = ?

So,

400 m = 0*9.0 sec + (1/2)*a*9.0^2

a = 400*2/9.0^2

a = 9.9 m/sec^2

2.

Again Using 2nd kinematic equation

h = U*t + (1/2)*a*t^2

(Here downward direction is positve, So)

h = height of building = 60 m

U = initial velocity = 20 m/sec

a = acceleration due to gravity = +9.8 m/sec^2

So,

60 = 20*t + (1/2)*9.8*t^2

4.9*t^2 + 20t - 60 = 0

Solving above quadratic equation (time is always +ve, so taking +ve root of above equation)

t = [-20 + sqrt (20^2 - 4*4.9*(-60))]/(2*4.9)

t = 2.0 sec

3.

when both object will pass each other, than

distance traveled by 1st object from ground = distance traveled by 2nd object from ground

h1 = h2

from 2nd kinematic equation

h1i + U1*t + 0.5*a*t^2 = h2i + U2*t + 0.5*a*t^2

h1i + U1*t = h2i + U2*t   

60 - 10*t = 0 + 40*t

t = 60/(40 + 10) = 1.2 sec

So after 2 sec both object will pass each other

distance traveled in this time by 2nd object will be

h2 = h2i + U2*t + 0.5*a*t^2

h2 = 0 + 40*1.2 - 0.5*9.8*1.2^2 = 40.94

h2 = 41 m

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