Lost my formula sheet, and at work without a book. Just need the formula\'s used

Question

Lost my formula sheet, and at work without a book. Just need the formula's used to get these questions, please specify what each symbol you write stand for thank you.

1. A motorist traveling at 110km/hr is being chased by a police car at 130 km/hr. If the police car starts from 1 kilometer back, how long does it take the police to intercept the motorist?

2. If you run a complete loop around an outdoor track (500m), in 100s, your average velocity is?

3. A bullet is fired from a gun at 300 m/s. It hits the ground 3 s later. At what angel (in degrees) above the horizon was the bullet fired? (Assume no air resistance).

3.

Explanation / Answer

here,

1)

speed of police car , v = 130 km/hr

distance , d = 1 km

let the time taken by the police car be t

using third equation of motion

v^2- u^2 = 2* a*s

130^2 = 2 * a * 1

a = 8450 km/h^2

using first equation of motion

v = u + a * t

130 = 8450 * t

t = 0.01538 hr

t = 55.38 s

the time taken by the police car is 55.38 s

2)

as the loop is complete,

the displacement is zero

then the average velocity is also zero

3)

initial speed of bullet , u = 300 m/s

time taken , t = 3 s

time to reach maximum height , t' = 1.5 s

let the angle be theta

v = u * sin(theta) - g * t

0 = 300 * sin(theta) - 9.8 * 3

theta = 5.62 degree

the angle above the horizontal is 5.62 degree

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