Question

a ball is dropped from the roof of a house. If the ball takes 1.1 seconds to fall, how many feet tall is the house?

Answer 1

Question

A ball is dropped from the roof of a house. If the ball takes 1.1 seconds to fall, how many feet tall is the house?

Solution

• Time taken by the ball to touch the ground (t) = 1.1 s

• Acceleration due to gravity (a) = 10 m/s²

Assuming the initial velocity of the ball to be zero

Using the Relation,

$\large{ \boxed{ \boxed{ \blue{ \sf{s = ut + \frac{1}{2}a {t}^{2} }}}}}$

Putting the values,we get :

$\large{ \tt{s = 0 \times 1.1 + \dfrac{1}{2} \times 10 \times {1.1}^{2} }} \\ \\ \large{ \leadsto \tt{s = \dfrac{1}{2} \times 11 \times 1.1 }} \\ \\ \large{ \leadsto \: \sf{s = \dfrac{12.1}{2} }} \\ \\ \large{ \leadsto \: \boxed{ \boxed{ \green{ \tt{s = 6.05 \: m}}}}}$

The height of the house is 6.5 m

Answer 2

You drop a ball ( free fall )

then the initial velocity u = 0m/s

time taken = 1.1 s

we are familiar with the gravity of Earth = 9.8N

we are to find the height of the house ,

h = ut + 1/2 gt²

h = 0× 1.1 + 1/2 ×( 9.8 ) × 1.1 ²

h = 0 + 4.8 × 1.21

h = 4.8×1.21

h = 5.808 m

The height of the house = 5.8 m ( approx )

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