Question

a particle is projected vertically upwards with the speed 20 m/s find the time after is at a height 15 m above the ground g=10m/s square

Answer 1

Answer:

Initial velocity= 20 m/s

Final velocity= 0 (on reaching its highest point the particle's velocity will become zero)

Acceleration due to gravity= -10 m/s^2 (as the particle is going opposite to gravity that is why it will be negative)

Height = 15 m

Here, we can also find time by putting the formula of height but in the formula of height there are two time or t which will make it confusing that is why we will use the formula of v = u + gt to find the time.

v = u + gt

=> 0 = 20 + (-10) × t

=> 0 = 20 - 10t

=> -20 = -10t

=> -20/-10 = t

=> 2 s = t

Thus, the time is 2 s.

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Answer 2

Given:

Initial velocity (u) of the particle = 20 m/s

Distance traveled (s) = 15 m

Acceleration due to gravity (g) = 10 m/s²

To find:

Time (t) after which the particle reaches a height of 15 m.

Solution:

• We have been given that the particle is projected upwards, hence, The value of acceleration due to gravity (g) will be negative, since the work is done against the force of gravity.

               Therefore, g = -10 m/s²

• Also, at the top most point, the final velocity will be 0 m/s as at the top most point, the potential due to gravity will be maximum hence v = 0 m/s.

Now, we have

v = 0 m/s   ; u = 20 m/s   ; s = 15 m   ; a = -g = -10 m/s²

Therefore

 $v = u + at$

Substituting the values in the equation, we get

 $0 = 20 + (-10)t$

$10t=20$

$or$

$t=2s$

Final answer:

Hence, the particle will reach a height of 15 m in 2 seconds.