A projectile is launched from ground level with an initial speed of 53.7 m/s. Find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (Ignore any effects due to air resistance.)

A projectile is launched with an initial velocity of 100 m/s at a 30° angle above the horizontal. Calculate the maximum height achieved by the projectile.

(a) From a balcony a child fires a toy arrow down to the ground below. The arrow has initial speed 12 m/s and is aimed at an angle of 30° below the horizontal. The arrow takes 1.2 seconds to hit the ground. (i) Calculate the initial horizontal (✰) and vertical (ŷ) velocity components of the arrow. (ii) Calculate the height of the balcony. (b) A projectile is launched with an initial speed of 75 m/s at an angle of 52° above the horizontal. If it lands at the same height from which it was launched, calculate how long the projectile remains in the air.

The maximum horizontal distance a boy can throw a ball is 50 m. Assume he can throw with the same initial speed at all angles. How high does he throw the ball when he throws it straight upward?