Could you please help with this question

Question

A student throws a set of keys vertically upward to his fraternity brother, who is in a window 3.95 m above. The brother's outstretched hand catches the keys 1.75 s later. (Take upward as the positive direction. Indicate the direction with the sign of your answer.)

(a) With what initial velocity were the keys thrown?

 

(b) What was the velocity of the keys just before they were caught?

Answer 1

a) Let's use the main kinematics equation;

H = V_oT + 1/2GT²

3.95 = V_o x 1.75 - 1/2 x 9.8 x 1.75²

3.95 = 1.75V_o - 15

V_o = 18.95/1.75 ≈ 10.83 m/s

b) V_f = V_o + gt

V_f = 10.83 - 9.8 x 1.75

V_f = -6.32 m/s (This means keys were caught when coming down, negative velocity)