Question

a ball is thrown vertically upwards with a velocity of 15m/s. calculate (i) the maximum height to which it rises, (ii) the total time it takes to return to the surface of the earth.

Answer 1

Note:

Italic writings are short notes to understand.

and italic with underlining is important notes

Step-by-step explanation:

Given the Initial velocity of the ball, u=15 m/s

Let the maximum height reached and the time taken to reach that height be H and t respectively.

Assumption: gravity = (g=9.8 m/s^2)

the final velocity of the ball at any maximum height will obviously be '0m/s'

so, v= 0m/s

Data we have till now

1. V= 0m/s
2. U = 15m/s
3. H =?
4. T=?
5. g = -9.8m/s (in this case gravity is negative due to the ball being thrown upwards it is the opposite in the case of it being thrown downwards)

we know, v^2 - u^2 = 2gH

0^2 - 15^2 = 2 x (−9.8) x H
we are taking gravity as negative as the ball is thrown against gravity.
0 - 225 = -19.6H
-225= -19.6H (cancel the minus from both sides )
225=19.6H

225/19.6= H (transpose)

H= 11.47m

now we know v= u +at

we will use this equation to find time 't'

v = u +at

0 = 15 + (-9.8)t we are taking gravity as negative as the ball is thrown against gravity.

0 = 15 - 9.8t

9.8t = 15 (transpose)

t= 1.53 seconds

Answer:

The height the ball reached = 11.47m

time it took for the ball to reach that height = 1.53 sec