Question

Hypothetically consider two balls thrown from the same place at the same time: the ball 1 with speed up to 30 m/s, and the ball 2, with speed of 50 m/s forming an angle of 30 ° with the horizontal. What is the distance between the balls at the instant when the first reaches its maximum height?

Answer 1

let

vo1 = 30 m/s
vo2 = 50 m/s
theta = 30 degrees

time taken for the first ball to reach maximum height, t1 = vo1y/g

= 30*sin(30)/9.8

= 1.5306 s

delta_x = t1*(vo2x - vo1x)

= 1.5306*(50*sin(30) - 30*sin(30) )

= 15.3 m

y1_max = vo1y^2/(2*g)

= (30*sin(30))^2/(2*9.8)

= 11.48 m

y2 = vo2y*t1 + (1/2)*(-g)*t1^2

= 50*sin(30)*1.5306 + (1/2)*(-9.8)*1.5306^2

= 26.8 m

delta_y = y2 - y1_max

= 26.8 - 11.48

= 15.3 m

distance between the balls at the instant when the first reaches its maximum height = sqrt(delta_x^2 + delta_y^2)

= sqrt(15.3^2 + 15.3^2)

= 21.6 m <<<<<<<<<--------------------Answer