Question

Help me pls

“A ball is projected vertically upwards with a velocity 30m/s. After what time
it is 40 m high from the point of projection? Take g 10 m/s.”

Answer 1

H = V t - 1/2 g t^2 V =vertical speed up and g is directed downwards

40 = 30 t - 5 t^2

8 = 6 t - t^2 divide by 5

t^2 - 6 t + 8 = 0

[6 +- (36 - 32)^1/2 ] / 2 = 2 or 4

Check (4 will mean the ball has reached max height and is moving down)

H = 30 * 4 - 5 * 16 = 120 - 80 = 40 m

2 of course will be the correct answer (6 - 2) / 2 = 2

H = 30 * 2 - 5 * 4 = 40 m