Answer:
(a) Height is 4.47 m
(b) Height is 4.37 m
Solution:
As per the question:
Initial velocity of teh ball, 
Angle made by the ramp, 
Distance traveled by the ball on the ramp, d = 5.00 m
Now,
(a) At any point on the projectile before attaining maximum height, the velocity can be given by the eqn-3 of motion:

where
H =
g = 

= 19.06 m/s
Now, maximum height attained is given by:


Height from the ground = 
(b) now, considering the coefficient of friction bhetween ramp and the ball,
:
velocity can be given by the eqn-3 of motion:


= 18.7 m/s
Now, maximum height attained is given by:


Height from the ground = 
Answer:

Explanation:
Given:
Initial velocity of the vehicle, 
distance between the car and the tree, 
time taken to respond to the situation, 
acceleration of the car after braking, 
Using equation of motion:
..............(1)
where:
final velocity of the car when it hits the tree
initial velocity of the car when the tree falls
acceleration after the brakes are applied
distance between the tree and the car after the brakes are applied.

Now for this situation the eq. (1) becomes:
(negative sign is for the deceleration after the brake is applied to the car.)
Answer:
The rate of change of the height is - 4 ft/s
Solution:
As per the question:
Height of the person, y = 5 ft
The rate at which the person walks away, 
Distance of the spotlight from the wall, x = 40 ft
Now,
To calculate the rate of change in the height,
of the person when, x = 10 m:
From fig 1.
![\Delta ABC[\tex] ≈ [tex]\Delta PQC[\tex]Thus[tex]\frac{BC}{AB} = \frac{PQ}{QC}](https://tex.z-dn.net/?f=%5CDelta%20ABC%5B%5Ctex%5D%20%E2%89%88%20%5Btex%5D%5CDelta%20PQC%5B%5Ctex%5D%3C%2Fp%3E%3Cp%3EThus%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cfrac%7BBC%7D%7BAB%7D%20%3D%20%5Cfrac%7BPQ%7D%7BQC%7D)

xy = 200 (1)
Differentiating the above eqn w.r.t time t:

Thus
(2)
From eqn (1):
When x = 10 ft
10y = 200
y = 20 ft
Using eqn (2):

Answer:
t = 5.05 s
Explanation:
This is a kinetic problem.
a) to solve it we must fix a reference system, let's use a fixed system on the floor where the height is 0 m
b) in this system the equations of motion are
y = v₀ t + ½ g t²
where v₀ is the initial velocity that is v₀ = 0 and g is the acceleration of gravity that always points towards the center of the Earth
e) y = 0 + ½ g t²
t = √ (2y / g)
t = √(2 125 / 9.8)
t = 5.05 s