Question

A balloon is rising with a velocity of 10 m/s. When it is at a height of 40 m above the earth, a packet is dropped from it. By what time it will take to reach the ground?
1. 10 s
2. 5 s
3. 4 s
4. 2 s

Answer 1

Correct Answer - Option 3 : 4 s

CONCEPT:

• When a body moves in a straight line under constant acceleration, it follows three equations of motion.
• All unknowns are found by these equations.

1. v = u + at;
2. s = ut + (1/2) at2 
3. v2 = u2 + 2as

where u is initial velocity, v is final velocity, a is constant acceleration, t is time and s is displacement.

CALCULATION:

Taking upward direction as +ve and downward -ve.

Given: 

A balloon is rising with a velocity of 10 m/s. So when a packet is released its initial velocity will be the same as the ballon i.e. 15 m/s. So

u = 10 ms-1;  h = -40 m; a = -g = -10 ms-2

s = ut + (1/2) at2 ​

-40 = 10 × t + (1/2) (-10) t2 ​

Solving equation t = -2 (not possible) and 4

So t = 4 sec

Hence the correct answer is option 3.