Question

A ball thrown vertically upward with a a speed of 19.6 m/s from the top of the tower and returns to the earth in 6 second. find the height of the tower.​

Answer 1

Answer:

58.8 metres is the required height of the tower .

Explanation:

According to the Question

It is given that ball thrown vertically upward with a a speed of 19.6 m/s from the top of the tower and returns to the earth in 6 second. we need to calculate the height of the tower . obviously the height of tower is equal to the day distance covered by the ball in given time interval.

So , using Kinematics Equation

Acceleration due to gravty is 9.8m/s²

• h = ut+½gt²

where,

h denote height of tower

u denote initial velocity

t denote time taken

g denote acceleration due to gravity

substitute the value we get

➻ h = 19.6×6 + ½×(-9.8) × 6² {as accⁿ due to gravity is acting in. downward direction)

➻ h = 117.6+ ½ × (-9.8)×36

➻ h = 117.6+ (-9.8)×18

➻ h = 117.6 - (9.8×18)

➻ h = 117.8 - 176.4

➻ h = -58.8m

➻h = 58.8 (as height cannot negative and its show that the ball covered 58.8 m distance from the top of the tower).

• Hence, the height of the tower is 58.8 metres

Answer 2

Answer:

Given :-

• A ball thrown vertically upward with a speed of 19.6 m/s from the top of the tower and returns to the earth in 6 seconds.

To Find :-

• What is the height of the tower.

Formula Used :-

$\clubsuit$ Second Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{h =\: ut + \dfrac{1}{2}gt^2}}}$

where,

• h = Height
• u = Initial Velocity
• t = Time Taken
• g = Acceleration due to gravity

Solution :-

Given :

• Initial Velocity (u) = 19.6 m/s
• Time Taken (t) = 6 seconds
• Acceleration due to gravity (g) = - 9.8 m/s²

According to the question by using the formula we get,

$\longrightarrow \sf h =\: (19.6)(6) + \dfrac{1}{2} \times (- 9.8)(6)^2$

$\longrightarrow \sf h =\: 19.6 \times 6 + \dfrac{1}{2} \times - 9.8 \times 6 \times 6$

$\longrightarrow \sf h =\: 117.6 + \dfrac{1}{2} \times - 58.8 \times 6$

$\longrightarrow \sf h =\: 117.6 + \dfrac{1}{2} \times - 352.8$

$\longrightarrow \sf h =\: 117.6 + ( - 176.4)$

$\longrightarrow \sf h =\: 117.6 - 176.4$

$\longrightarrow \sf h =\: - 58.8\: \: \bigg\lgroup \small\sf\bold{\pink{Height\: can't\: be\: negative\: (-\: ve)}}\bigg\rgroup$

$\longrightarrow \sf\bold{\red{h =\: 58.8\: m}}$

${\small{\bold{\underline{\therefore\: The\: height\: of\: the\: tower\: is\: 58.8\: m\: .}}}}$