Please help me to solve this problem.
A body is projected vertically upwards with a velocity 20m/s. find the maximum height reached by the body.(g=10m/sec2)
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as v=o and u=20m/s so by using equation v^2-u^2 = 2as , 0^2- 20^2 = 2(-10)s= 400/20=20 m/s
To find the maximum height reached by the body, we can use the equations of motion.
The first equation of motion to consider is:
v = u + at
Where:
v = final velocity (0 m/s at the maximum height)
u = initial velocity (20 m/s upwards)
a = acceleration (in this case, acceleration due to gravity = -10 m/s^2, as it acts in the opposite direction to the motion)
t = time taken to reach the maximum height (this is what we need to find)
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Substituting the given values:
v = 0 m/s
u = 20 m/s
a = -10 m/s^2
t = (0 - 20) / -10
t = 2 seconds
So, it takes 2 seconds for the body to reach the maximum height.
Now, we can use the second equation of motion to find the maximum height (h) reached by the body. The equation is:
s = ut + (1/2)at^2
Where:
s = displacement (in this case, the maximum height)
u = initial velocity (20 m/s upwards)
t = time taken to reach the maximum height (2 seconds)
a = acceleration due to gravity (-10 m/s^2)
Substituting the values, we get:
s = (20 * 2) + (1/2)(-10)(2^2)
s = 40 - 20
s = 20 meters
Therefore, the maximum height reached by the body is 20 meters.