Question

1. Write the three equation of motion for freely falling bodies and write the value of g.

2. A cricket ball is dropped from a height of 20 metres. [5 MARKS]

(a) Calculate the speed of the ball when it hits the ground

(b) Calculate the time it takes to fall through this height.

Answer 1

Three equation and value of g: 2 Marks
Each problem: 1.5 Mark

1. $v=u+gt$
$v^2=u^2+2gh$
$h=ut+\frac{1}{2}g{t}^2$
$(g=10m/s^2)$

2. (a) Here, Initial speed, u = 0

Final speed, v = ? (To be calculated)

Acceleration due to gravity, $g=10m/s^2$ (Ball comes down)

And, Height, h = 20 m

Now, we know that for a freely falling body:

$v^2=u^2+2gh$

So, $v^2=(0{)}^2+2\times 10\times 20$

$v^2=400$

$v=\sqrt{400}$

or $v=20m/s$

Thus, the speed of cricket ball when it hits the ground will be 20 metres per second.

(b) Now, Initial speed, u = 0

Final speed, v = 20 m/s (Calculated above)

Acceleration due to gravity, $g=10m/s^2$

And, Time, t = ? (To be calculated)

Putting these values in the formula:

$v=u+gt$

we get: $20=0+10\times t$

$10t=20$

$t=\frac{20}{10}$

$t=2s$

Thus, the ball takes 2 seconds to fall through a height of 20 metres.