Question

1) Suppose that a runner on a straight track covers a distance of 1 mile in exactly 4min. what was its average velocity in
(i) mih-1 (iii) cms-1
(ii) fts-1 (iv) kmh-1


2) A bullet of mass 10g traveling horizontal at a speed of 100 ms-1 embeds itself in a block of woods mass 990g suspended by a string so that it can swing freely.

Find the vertical height through which block rises.

Answer 1

1. These are exercises in changing dimensions. Four minutes is (1/15 mile) One mile is 4 minutes is therefore
1.0 mile/(1/15 h) = 15 mi/h

For ft/s, multiply that by
(5280 ft/mile)/(3600 sec/h), which happens to be 22/15 ft*h/s*mi, and you get 22 ft/s

Now you do the others; you need to develop the ability to do these yourself.

2. This is the classic ballistic pendulum problem. Use conservation of momentum to get the speed V of the block with embedded bullet, before swinging begins.
10*100 g m/s = V*1000 g
V = 1 m/s
Now used conservation of energy to determine how high (H) the pendulum swings.
(1/2) M V^2 = M g H
H = V^2/(2g)