A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

43. A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?




a)

$y_f=0m\\y_o=h=4m\\a=-g=-9.8m/s^2\\ t=1.5sv_o=?\\v_f=?$

We have the necessary values for finding both initial velocity and the final velocity;

So, the initial velocity can be found using the following equation when the keys are caught at t=1.5s

$y_f=y_o+v_ot+\frac{at^2}{2}$

$y_f=y_o+v_ot-\frac{gt^2}{2}$

$0m=4m+v_o(1.5s)-\frac{9.8m/s^2*(1.5s)^2}{2}$

solving for vo

$v_o=10.01m/s$

b) The velocity of the keys just before they were caught;

$v_f=v_o+at=10m/s-9.8m/s^2(1.5s)\\ v_f=-4.7m/s$