Answer :
Answer:
10.8 m/s,-39.7º below the horizontal
Explanation:
let V be the initial velocity
the horizontal component is ... V cos (65.0)
the vertical component is ... V sin(65.0)
for horizontal ... d=V*t=Vcos (65.0)*t
17=V*1/2*t
34=V*t
for vertical ... h=-1/2*g*t^2+V sin(65.0)*t
5=-4.90m/s^2*t^2+(√3/2)Vt
substituting for V t ..
5.00 m - 17 √3 m = -4.9 m/s² t²
(5.00 - 17 √3) / -4.90 = t²
2.17 s = t
(a) 34.0 m = V * 2.17 s
V = 16.6 m/s
use the horizontal and vertical equations of motion to find the flight time (t)
then substitute back to find the initial velocity (V)
let v be the final velocity
finding the components of the final velocity
the horizontal component is the same as the initial velocity vh = V cos(65.0º) = 16.6 / 2 = 8.30 m/s
for the vertical component v_v = V sin(65.0º) - g*t
v_v = (16.6 * √3 / 2) - (9.80 * 2.17) = - 6.89 m/s
the horizontal component is unchanged from the initial velocity (no horizontal acceleration)
use gravitational acceleration to find the vertical component
use Pythagoras to find the magnitude of the final velocity
(b) v = √(vh² + v_v²) = 10.8 m/s
use trig to find the angle
the tangent of the angle is tan(Θ) = v_v / vh = -.830
Θ = -39.7º
the ball is moving downward