Question

56. A ball is projected vertically upwards with a certain
speed. Another ball of the same mass is
projected at an angle 60° to the vertical with the
same initial speed. The ratio of their potential
energies at highest points of their journey, will be
(1) 1:1 (2) 2:1 (3) 3:2 (4) 4:1​

Answer 1

Answer:

0

Explanation:

at highest point velocity is zero then potential energy is zero

Answer 2

Case: 1
Max Height = (u² sin²90°)/2g = u²/2g .....(1)
{sin 90° is 1, therefore 1×1 =1}

Case: 2
since the ball is thrown 60° from the vertical, therefore, angle from the horizontal is 90°-60° = 30°

Max Height = (u²sin²30)/2g = (u² × 1/2 × 1/2) / 2g
= (u²/4)/2g = u²/8g ......(2)

Therfore,
Potential energy of the 1st ball at its highest point =(mg u²/2g)......(3)

Potential energy of the 2nd ball at its highest point
= (mg u²/8g).......(4)

Dividing eq. (3) by eq. (4), we get,

mg u²/2g ÷ mg u²/8g = 4


Hence, the ratio of their potential energies at their highest points of their journey will be 4:1


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