A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is 10 m/s in the downward direction , what will be the height attained by the stone and how much time will it take to reach there ?

Question

Answer

U = 5 m/s
a = -10 m/s
v = 0 ( at highest point )
hight attend by stone = s = v² - u² / 2a
s = 0² - 5² / 2 x -10
s = -25 /-20
s = 25/20 ( minus , minus = plus
s= 1.25 meter
time it will take to reach there =
v= u + at
0 = 5 + (-10 x t )
-5 = -10t
-5 / -10 = t
t = 0.5 second

Answer

Analysis:

To solve this problem, we can use the equations of motion to determine the height attained by the stone and the time it takes to reach that height.

Given:

Initial velocity (u) = 5 m/s (upward)
Acceleration (a) = 10 m/s² (downward)

Using the equations of motion:

We can use the following equations of motion to solve this problem:

1. v = u + at
2. v² = u² + 2as
3. s = ut + 0.5at²

Calculating the time taken to reach the maximum height:

Since the stone is thrown upwards, its final velocity at the maximum height will be zero (v = 0). The initial velocity (u) is given as 5 m/s (upward), and the acceleration (a) is given as 10 m/s² (downward).

Using the first equation of motion:
0 = 5 - 10t
10t = 5
t = 5/10
t = 0.5 seconds

Therefore, it takes 0.5 seconds for the stone to reach the maximum height.

Calculating the height attained by the stone:

To calculate the height attained by the stone, we can use the third equation of motion. We already know the initial velocity (u = 5 m/s) and the time taken to reach the maximum height (t = 0.5 seconds). We need to find the displacement (s).

Using the third equation of motion:
s = ut + 0.5at²
s = 5 * 0.5 + 0.5 * 10 * (0.5)²
s = 2.5 + 0.5 * 10 * 0.25
s = 2.5 + 1.25
s = 3.75 meters

Therefore, the height attained by the stone is 3.75 meters.

Conclusion:

The stone takes 0.5 seconds to reach the maximum height of 3.75 meters.

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