To solve the projectile motion problem, the initial speed is calculated using the range formula for projectile motion, and the vertical speed at maximum height is zero.
The student's question concerns the determination of two key variables: the initial speed of a projectile launched at a 30° angle and its speed at the maximum height it reaches.
Given that the horizontal displacement of the projectile is 50 meters and the acceleration due to gravity is 10 m/s2, we can solve this problem using the principles of projectile motion.
To find the initial speed (Vi), we use the formula for horizontal range in projectile motion:
R = Vi2 * sin(2θ) / g
Since R = 50 m, g = 10 m/s2 and θ = 30°, we can solve for Vi.
For the second part of the question, at the maximum height, the vertical component of velocity is zero. However, the horizontal component of velocity remains the same, since gravity does not affect the horizontal motion. Therefore, the speed at maximum height is equal to the horizontal component of the initial speed.