Question

A ball is thrown vertically upward with velocity of 10m/s. calculate the height attained by the ball and the time taken by it to reach the highest point if the acceleration of the ball is -10m/s^2 during its motion.​

Answer 1

Answer:

Time taken = 1 sec

Height = 5 m

Explanation:

As per the provided information in the given question, we have:

• A ball is thrown vertically upward with velocity of 10m/s.

Thus, Initial velocity of the ball is 10 m/s.

In order to find the time taken by the ball to reach the highest point, We need to find height first. Then, We can find time taken using the first equation of free fall.

• Let the maximum height the ball will reach be h. & Let the maximum height's final velocity be v.

Finding height using the third equation of motion :

$\begin{gathered}\longmapsto \bf {v}^{2} - {u}^{2} = 2gh \end{gathered}$

Where,

• v denotes final velocity
• u denotes initial velocity
• g denotes gravity
• h denotes height

$\begin{gathered}\longmapsto \rm {0}^{2} - {10}^{2} = 2(-10) \times h \end{gathered}$

$\begin{gathered}\longmapsto \rm {0} - {100} = -20h \end{gathered}$

$\begin{gathered}\longmapsto \rm -20h= -100 \end{gathered}$

$\begin{gathered}\longmapsto \rm h= \dfrac{-100}{-20} \end{gathered}$

$\begin{gathered}\longmapsto \rm h=\cancel{ \dfrac{-100}{-20} } \end{gathered}$

$\begin{gathered}\longmapsto \rm h= 5 m \end{gathered}$

∴ Maximum height at which ball will reach is 5 m

Finding time taken :

Let the time taken by the ball to come reach the highest point be t.

Now, we have to find time taken, Using the first equation of free fall :

$\begin{gathered}\longmapsto \bf {v} = u + gt \end{gathered}$

Where,

• v denotes final velocity
• u denotes initial velocity
• g denotes gravity
• t denotes time

$\begin{gathered}\longmapsto \rm {v} = 10 - 10t \end{gathered}$

$\begin{gathered}\longmapsto \rm -10t = -10 \end{gathered}$

$\begin{gathered}\longmapsto \rm t = \dfrac{-10}{-10} \end{gathered}$

$\begin{gathered}\longmapsto \rm t = 1 \: sec \end{gathered}$

∴ The time taken by it to reach the highest point is 1 sec.