Answer:
vo = 13.74 m/s
Step-by-step explanation:
The goal is to find the initial velocity vo. According to the exercise, the maximum height that the ball will reach and the initial height will be respectively, yo = 1.5 m and ymax = 7 m, tmax will be equal to the time it takes for the ball to reach the maximum height. Having the equation:
vx = vo * cos∝o
clearing vo:
vo = vx/cos∝o
vy = vo * sin∝o + gtmax
0 = sin∝o * (vx/cos∝o) + gtmax
0 = vx * tan∝o + gtmax
gtmax = -vx * tan∝o
clearing tmax:
tmax = - (vx * tanao/g)
ymax = i + (vo * sin∝o) * tmax + (gtmax^2/2)
Replacing:
ymax = i - (vx^2 * tan^2∝o/2 * g)
clearing the angle a or:
∝o = arctan (((2 * g * (i - ymax)) / vx^2)^1/2)
substituting values:
∝o = arctan (((2 * (- 9.8) * (1.5 - 7)) / (9^2))) = 49.08 °
We find the initial speed with the following formula:
vo = vx/cos∝o = 9/cos49.08 ° = 13.74 m/s