Question

a ball is thrown upwards from the top of a tower 40 m high with a velocity of 10m/s,find the time when it strikes the ground.​

Answer 1

Answer:

Time taken by ball to reach ground

= 4 seconds

Step by step explanations :

given that,

a ball is thrown upwards from the top of a tower 40 m high with a velocity of 10m/s

here,

initial velocity of the ball = 10 m/s

final velocity when it reaches at its maximum height = 0 m/s

[it will at rest]

gravitational acceleration(g) = -10 m/s²

by the gravitational equation of motion,

v² = u² + 2gh

where,

h is height attained by the ball from the tower

putting the values,

0² = 10² + 2(-10)h

-20h = -100

h = -100/-20

h = 5 m

time taken by the ball to reach maximum height from the tower = t

v = u + gt

0 = 10 + (-10)t

-10t = -10

t = -10/-10

t = 1 s

so,

time taken by ball to reach maximum height from the tower = 1 seconds

now,

height of the ball from tower = 5 m

so,

height of the ball from the ground

= 40 + 5

= 45 m

now,

at its maximum height,

velocity of the ball will 0

let it be initial velocity,

so,

initial velocity(u) = 0 m/s

height(h) = 45 m

gravitational acceleration(g) = -10 m/s²

also by the gravitational equation of motion,

h = ut + ½ gt²

where,

t is the time taken by the ball to reach the ground from its maximum height

initial velocity(u) = 0 m/s

height(h) = 45 m

gravitational acceleration(g) = 10 m/s²

putting the values, 0(t)

45 = 0(t) + ½ × (10) × t²

5t² = 45

t² = 45/5

t² = 9

t = 3 s

so,

time taken by ball to reach ground from its maximum height

= 3 seconds

now,

total time taken = 3 + 1

= 4 s

so,

total time taken by reaching ground from its initial position

= 4 seconds

Answer 2

$\huge\sf\underline{Answers}$

$\bf\huge\boxed{4\:sec}$

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Given—

u = 10 m/s

a = - 10 m/s²

s = - 40 m

➡at the point where stone strikes the ground

Substituting in

$s \: = ut + \frac{1}{2} at {}^{2}$

=> - 40 = 10t - 5t²

=> 5t² - 10t - 40 = 0

=> t² - 2t - 8 = 0

Solving the quadratic we get

t = 4 sec | t= - 2 sec

Since time cant be negative

therefore the time taken to strike is 4 sec.

$\huge{\red{\ddot{\smile}}}$