Answer:
s = ut + at²/2
82 = 0*t = 10*t²/2
t = 4.0s
s=ut
53 = H*4
H=13.25 m/s - Horizontal velocity
v² = u²+2as
v² = 0 + 2*10*82
v =40.5 m/s - vertical velocity
vector sum
R²= V²+H²
R² = 40.5²+13.25²
R = 42.6m/s
Explanation:
horizontal velocity of the ball stays constant throughout the time because there is no horizontal forces acting on the ball to change its velocity ( according to newtons second law of motion). but the vertical velocity of the ball will increase (initially it is zero) because the gravitational force is acting vertically downward upon the ball. so the final velocity will be the vector sum of horizontal and vertical velocities at the point of impact with the ground. we already know the horizontal distance(53m) and vertical distance (82m) that the ball travels. there is no acceleration horizontally but the vertical acceleration is g = 9.8 m/s²(10m/s² approximately). so first from the vertical movement we can find the time of flight of the ball to hit the ground by the equation (s = ut + at²/2) . and also the vertical velocity at impact can also be found( v² = u²+2as) . to find the horizontal velocity we can use (s=ut) here t is the time of flight of the ball.
after finding the two velocities we can get the vector sum of the two. the velocities are normal to each other.
so the final velocity of the ball R will be
R² = V²+H² V=vertical velocity, H = Horizontal velocity
