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timurjin [86]
4 years ago
6

A ball thrown vertically upward is caught by the thrower after 2.00 s. Find (a) the initial velocity of the ball and (b) the max

imum height the ball reaches.
Physics
1 answer:
ankoles [38]4 years ago
4 0

Answer:

a)  9.8 m/s

b) 4.9 m

Explanation:

This problem is a good example of Vertical motion, where the main equations for this situation are:  

y=y_{o}+V_{o}t-\frac{1}{2}gt^{2} (1)  

V^{2}={V_{o}}^{2}-2gy (2)  

Where:  

y is the height of the ball at a given time

y_{o}=0m is the initial height of the ball (assuming the hand of the thrower the origin of the system)  

V_{o} is the initial velocity of the ball

V is the final velocity of the ball

t=2s is the time it takes for the ball to make the complete movement (from the moment it is thrown until it falls back into the pitcher's hands)

g=9.8 m/s^{2} is the acceleration due to gravity  

Knowing this, let's begin with the answers:

<h3>a) Initial velocity </h3>

In order to find the initial velocity V_{o} of the ball, we will use equation (1) and t=2s, taking into account that y=0 m and y_{o}=0m at this given time:

0=0+V_{o}t-\frac{1}{2}gt^{2} (3)  

Isolating V_{o}:

V_{o}=\frac{1}{2}gt (4)  

V_{o}=\frac{1}{2}(9.8 m/s^{2})(2 s) (5)  

Then:

V_{o}=9.8 m/s (6)  

<h3>b) Maximum height </h3>

In this part, we will use equation (2), knowing the value of the height is maximum when V=0. So, we will name this height as y_{max}:

0={V_{o}}^{2}-2gy_{max} (7)  

Isolating y_{max}:

y_{max}=\frac{{V_{o}}^{2}}{2g} (8)  

y_{max}=\frac{{(9.8 m/s)}^{2}}{2(9.8 m/s^{2})} (9)  

Finally:

y_{max}=4.9 m

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