a rock is thrown vertically upwards with an initial velocity of 30 m/s. Neglecting air resistance, calculate
a) the maximum height reached
b) the time taken to reach maximum height
PLEASE help with this
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a rock is thrown vertically upwards with an initial velocity of 30 m/s. Neglecting air resistance, calculate
To solve this problem, we can use the equations of motion for an object undergoing vertical motion in the absence of air resistance.
a) To find the maximum height reached by the rock, we can use the equation for displacement:
Δy = V0y * t - 0.5 * g * t^2
Where:
Δy = change in vertical position (maximum height)
V0y = initial vertical velocity
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Since the rock is thrown vertically upwards, the initial velocity V0y is equal to 30 m/s (magnitude) but in the opposite direction. Therefore, V0y = -30 m/s.
At the maximum height, the vertical velocity becomes zero. So, V0y * t - 0.5 * g * t^2 = 0.
Substituting the values, we get:
-30t - 0.5 * 9.8 * t^2 = 0
Simplifying this equation will give us the value of t, which we can then substitute back into the original equation to find the maximum height.
b) To calculate the time taken to reach the maximum height, we can use the equation for vertical velocity:
Vf = V0y - g * t
At the maximum height, Vf = 0. We can substitute this into the equation and solve for t:
0 = -30 - 9.8 * t
Simplifying this equation will give us the time taken to reach the maximum height.
To solve these equations, we can use a scientific calculator or a mathematical software. Enter the equations and solve for the desired values.