In his first attempt, a long jumper took off from the spring board with a speed of 8 ms(^{-1}) at 30° to the horizontal. He makes a second attempt with the same speed at 45° to the horizontal. Given that the expression for the horizontal range of a projectile is (frac{u^2 sin 2theta}{g}) where all the symbols have their usual meanings, show that he gains a distance of 0.8576 m in his second attempt. [g = 10ms(^{-2})]
Explanation
1st Attempt R = (frac{U^2 sin 2 theta}{g} = frac{8^2 sin 60}{10} = 5.5424m)
2nd Attempt R = (U^2sin 2 theta)
= (frac{8^2sin 90}{10}) = 6.4m
Gain = 6.4 – 5.5425 = 0.8576m