# 20230814 kinematics hw

```8.14 δ½δΈοΌ
1.
(a) If π‘1 is the time taken for the stone to reach the bottom of the canyon and π‘2 is the
time for the sound wave produced to reach the top of the canyon:
(i) write down the equations that determine π‘1, and π‘2, neglecting air resistance
(ii) calculate the exact value of π‘1
(iii) calculate the exact value of π‘2
(iv) deduce the depth of the canyon
(b) If the stone is initially thrown with velocity π’ horizontally into the canyon, what
differences will arise in the answers to question (a)(i)?
(c) If the stone is thrown vertically upwards with velocity π’, how will this alter the answers
to question (a)(i)?
2.
Rain is falling vertically at 8.0 m s−1. The rain drops make tracks on the side of a car
window at an angle of 30&deg; below the horizontal. Calculate the speed of the car, giving a
full explanation.
3.
A car starts from rest at time π‘ = 0 and travels with constant acceleration π1, for time π‘1 .
From time π‘1 to π‘2 it travels with constant speed π’ . After π‘2 a retarding acceleration is
applied, of initial magnitude π2, which decreases linearly to zero at time π‘3 when the car
comes to rest.
Sketch the following graphs: (i) acceleration-time
(ii) velocity-time
(iii) distance-time
4.
5.
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