Can anyone help with this physics problem?

Question

Snowballs are thrown with a speed of 13 m/s from a roof 7 m above the ground. Snowball A is thrown straight downward; snowball B is thrown in a direction 25 degrees above the horizontal. (A) Is the landing speed of snowball A greater than, less than, or the same as the landing speed of snowball B? Explain. (B) Verify your answer to part a by calculating the landing of both snowballs.

Answer 1

Both balls land with the same speed. Ball A just arrives sooner and at a different angle.

Equation of motion of each is
vy(t)=v0*sin(th)-g*t
vx(t)=v0*cos(th)

and y(t)=7+v0*sin(th)-.5*g*t^2
x(t)=v0*cos(th)*t

be sure to set the angle of the downward throw at 270 degrees and the other at 25 degrees.

Since v0=13 (magnitude since the angle will set the correct sign)

for 270 degrees
vy(t)=-13-g*t
and
0=7-13*t-.5*g*t^2
using g=9.81 solve for t
t=.458 seconds
so vy(.458)= -17.3 m/s

for th=25
0=7+13*sin(25)-.5*g*t^2
t=1.85 seconds
vy(t)= -12.7
and vx=11.78
so the resultant speed is
17.3


j