To determine the maximum height reached by the object, we can analyze the motion in the vertical direction.
The initial velocity of the object can be broken down into its horizontal and vertical components:
Initial horizontal velocity (Vx) = 60 m/s * cos(30°) Initial vertical velocity (Vy) = 60 m/s * sin(30°)
The object will reach its maximum height when the vertical velocity becomes zero, as it momentarily stops moving upwards before starting to descend.
In vertical motion, the equation for calculating the time taken to reach maximum height (t) can be derived from the equation:
Vy = Vy0 + gt
Where: Vy = Final vertical velocity (0 m/s at maximum height) Vy0 = Initial vertical velocity (60 m/s * sin(30°)) g = Acceleration due to gravity (-9.8 m/s²)
0 = 60 m/s * sin(30°) - 9.8 m/s² * t
Solving for t:
60 m/s * sin(30°) = 9.8 m/s² * t t = (60 m/s * sin(30°)) / 9.8 m/s²
Now that we have the time taken to reach the maximum height, we can find the maximum height (h) using the equation for vertical displacement:
h = Vy0 * t + (1/2) * g * t²
Substituting the values:
h = (60 m/s * sin(30°)) * [(60 m/s * sin(30°)) / 9.8 m/s²] + (1/2) * (-9.8 m/s²) * [(60 m/s * sin(30°)) / 9.8 m/s²]²
Calculating this expression will give you the maximum height reached by the object.