Respuesta :
Answer:
The time when the object to reach its maximum height is 4.25 sec.
The maximum height is 187.50 m.
Explanation:
Given that,
Initial velocity = 41.65 m/s
Height = 99 m
The projectile motion model h(t) is
[tex]h(t)=-4.9t^2+v_{0}t+h_{0}[/tex]
Put the value in the equation
[tex]h(t)=-4.9t^2+41.65t+99[/tex]
On differentiating equation (I)
[tex]\dfrac{dh}{dt}=v=-9.8t+41.65[/tex]
We need to calculate the time at maximum height
The velocity is zero at maximum height,
So, [tex]-9.8t+41.65=0[/tex]
[tex]t =\dfrac{-41.65}{-9.8}[/tex]
[tex]t=4.25\ sec[/tex]
We need to calculate the maximum height
Put the value of t in equation (I)
[tex]h_(max)=-4.9\times(4.25)^2+41.65\times4.25+99[/tex]
[tex]h_{max}=187.50\ m[/tex]
Hence, The time when the object to reach its maximum height is 4.25 sec.
The maximum height is 187.50 m.
