Question

A balloon is going upwards with velocity 12
m/sec. It releases a packet when it is at a
height of 65 m from the ground. How much
time the packet will take to reach the ground
(g
=10m/sec)
1) 5 sec 2) 6 sec 3) 7 sec 4) 8 sec

Answer 1

Answer:

option (1) 5 sec

Explanation:

Let, us assume the downward direction as positive and upward direction as negative

then,

→  Initial velocity of packet , u = -12 ms⁻¹

→  distance traveled by packet, s = 65 m

→  acceleration due to gravity , g = 10 ms⁻²

We need to find the time taken ( t ) by packet to reach the ground

so,

Using second equation of motion

⇢ s = u t + 1/2 a t²

putting known values

⇢ 65 = (- 12) t + 1/2 (10) t²

⇢ 65 = -12 t + 5 t²

⇢ 5 t² - 12 t - 65 = 0

Solving the quadratic equation formed

⇢ 5 t² - 25 t + 13 t - 65 = 0

⇢ 5 t ( t - 5 ) + 13 ( t - 5 ) = 0

⇢ ( 5 t + 13 ) ( t - 5 ) = 0

⇢ t = -13 / 5  or t = 5

since,  time cannot be negative

therefore we will accept the value of t = 5

Hence,

⇢ t = 5 sec

Therefore,

Packet will take 5 seconds to reach the ground.