Question

Lavanya throws a ball upwards, from a rooftop, which is 20 m above from ground. It will reach a maximum height
and then fall back to the ground. The height of the ball from the ground at time is h, which is given by h=-4t+16+ + 20.
(i) What is the height reached by the ball after 1 second?
(a) 64 m (C) 32 m (b) 128 m (d) 20 m

(ii) What is the maximum height reached by the ball?
(a) 54 m (c) 36 m (b) 44 m (d) 18 m

(iii) How long will the ball take to hit the ground?
(a) 4 seconds (c) 5 seconds (b) 3 seconds (d) 6 seconds

(iv) What are the two possible times to reach the ball at the same height of 32 m?
(a) I and 3 seconds (c) I and 2 seconds

(v) Where is the ball after 5 seconds
(a) at the ground (c) at highest point (b) 1 and 4 seconds (d) 1 and 5 seconds (b) rebounds (d) fall back
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Answer 1

Answer:

i) Ans - d) 20 m

ii)Ans - c) 36 m

iii)Ans - b) 3 seconds

iv)Ans - a) 1 and 3 seconds

v)Ans - a) at the ground

Explanation:

h = -4t² + 16t + 20

t = 1

=> h = -4 + 16 + 20

=> h = 32

height reached by the ball after 1 second = 32 m

h = -4t² + 16t + 20

dh/dt = -8t + 16

dh/dt = 0

=> t = 2

d²h/dt² = -8 < 0 hence max height at t = 2

h = -4(2)² + 16*2 + 20

=> h = 36

Max height = 36 m

height at ground = 0

-4t² + 16t + 20 = 0

=> t² - 4t - 5 = 0

=> (t - 5)(t + 1) = 0

=> t = 5 , - 1

Hence ball take 5 secs to hit the ground

-4t² + 16t + 20 = 32

=> t² -4t - 5= - 8

=> t² - 4t + 3 = 0

=> (t 1)(t - 3) = 0

1 and 3 sec

ball after 5 seconds at the ground.

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