Question

If a frog jumps with an initial velocity of 100m/s at an angle of 60°. a. What is the frog’s x and y components of velocity? b. How high will the frog get? c. How long will it take the frog to reach its maximum height?

Answer 1

Explanation:

It is given that,

Initial velocity of frog, u = 100 m/s

It jumps at an angle of 60 degrees.

(a) Let $v_x\ and\ v_y$ are the x and y components of velocity. It can be calculated as :

$u_x=u\ cos\theta$

$u_x=100\times \ cos(60)$

$u_x=50\ m/s$

$u_y=u\ sin\theta$

$u_y=100\times \ sin(60)$

$u_y=86.6\ m/s$

(b) Let y is the maximum height reached by the frog. It can be calculated using the third equation of motion as :

At maximum height, $v_y=0$

$v_y^2-u_y^2=2ay$ and a = -g

$-u_y^2=-2g$

$y=\dfrac{u_y^2}{2g}$

$y=\dfrac{86.6^2}{2\times 9.8}$

y = 382.63 meters

(c) Let t is the time taken by the frog to reach its maximum height. It can be calculated as :

$v_y=u_y-gt$

$0=u_y-gt$

$t=\dfrac{u_y}{g}$

$t=\dfrac{86.6\ m/s}{9.8\ m/s^2}$

t = 8.83 seconds

Hence, this is the required solution.