Answer:
- The maximum height reached by the ball is 45.92 m
- Time taken to fall down to half of its height is 2.2 s
Explanation:
Given;
initial velocity of the ball, u = 30 m/s
final velocity of the ball at the highest point, v = 0
The maximum height reached by the ball is calculated as;
v² = u² - 2gh
where;
h is the maximum height reached by the ball
0 = 30² - (2 x 9.8)h
19.6h = 900
h = 900 / 19.6
h = 45.92 m
Time taken to fall to half of its height is calculated as;
when falling down, the final velocity v becomes the initial velocity = 0.
Apply the following kinematic equation;
h = ut + ¹/₂gt²
h = 0 + ¹/₂gt²
h = ¹/₂gt²
where;
h = 45.92 m is the maximum height reached
half of h = 45.92 / 2 = 22.96 m
22.96 = ¹/₂gt²

Answer:
100 m
Explanation:
Arthur and Betty should be walking the same amount of time if they start walking at the same time and stop when they meet = t
Speed of Arthur = 3 m/s
Speed of Betty = 2 m/s
Distance = Speed × time
Distance covered by Arthur = 3t
Distance covered by Betty = 2t
The distance covered by both of them will be 100 m

The speed of dog is 5 m/s
Spot is running back and forth at 5 m/s for 20 seconds
In 20 seconds the distance covered by the dog is

Explanation:
a. The force acting down is gravity, on Earth gravity is 10 m/s^2. When the skydiver jump, the acceleration will start out as -10 m/s^2, but it will eventually equals the air resistance , which is called terminal velocity.
Answer:
n = 1810
A = 25 mm
Explanation:
Given:
Lateral force amplitude, F = 25 N
Frequency, f = 1 Hz
mass of the bridge, m = 2000 kg/m
Span, L = 144 m
Amplitude of the oscillation, A = 75 mm = 0.075 m
time, t = 6T
now,
Amplitude as a function of time is given as:

or amplitude for unforce oscillation

or

or

Now, provided in the question Amplitude of the driven oscillation

the value of the maximum amplitude is obtained
thus,

Now, for n people on the bridge
Fmax = nF
thus,
max amplitude

or
n = 1810
hence, there were 1810 people on the bridge
b)
since the effect of damping in the millenium bridge is 3 times
thus,
b=3b
therefore,

or

or

or
A = 0.025 m = 25 mm