Projectile Motion

Question

A ball is thrown straight upward and returns to the thrower’s hand after 3.7 s in the air. A second ball is thrown at an angle of 45◦ with the horizontal. At what speed must the second ball be thrown so that it reaches the same maximum height as the first? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

Answer 1

Don't over think this one. The second ball needs to go up with the same initial speed as the first. We know that it loses that speed to gravity's pull in 1.85 seconds (the time of flight on the way up.) So that initial vertical speed is simply equal to the acceleration due to gravity times the time of the upward flight. To get the total speed, we put that vertical speed in as our vertical component in our velocity vector triangle and solve for the hypotenuse. This is a 45-45-90 triangle so you just multiply a short side by root two to get the total initial velocity.