Question

A body is projected vertically upwards with a velocity of 98 m/s.
find (i)the maximum height attained by the body and (ii) time
taken by body to reach the highest point. Take g = 9.8 m/s2

Answer 1

Required Answer :

• The maximum height attained by the body = 490 m
• Time taken by body to reach the highest point = 10 seconds

Given :

• Initial velocity = 98 m/s
• Final velocity = 0 m/s [The final Velocity becomes zero because the velocity at the topmost point is always zero.]
• Acceleration due to gravity = 9.8 m/s²

To find :

(i) The maximum height attained by the body

(ii) Time taken by body to reach the highest point.

Solution :-

Third equation of motion :-

• v² - u² = 2as

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration due to gravity
• s = distance/displacement

→ (0)² - (98)² = 2(- 9.8)(s)

→ - 9604 = - 19.6 × s

→ 9604 ÷ 19.6 = s

→ 490 = s

Maximum height = 490 m

(ii) Time = ?

First equation of motion :-

• v = u + at

where,

• t = time

→ 0 = 98 + (- 9.8)(t)

→ - 98 = - 9.8 × t

→ 10 = t

Time = 10 s

Answer 2

Answer:

Solution :-

Third equation of motion :-

v2 - u? = 2as

-

=

where,

. V = Final velocity

• u = Initial velocity

• a = Acceleration due to gravity

• s = distance/displacement

.

=

.

=

+ (0)2 - (98)2 = 2(- 9.8)(s)

→-9604 = - 19.6 xs

→ 9604 - 19.6 = s

→ 490 = 5

Maximum height = 490 m