Question

what is the maximum height obtained by a 125g apple that is slung from a slingshot at an angle 78° from the horizontal with an initial velocity of 18 m/s

Answer 1

$Vy = V*sin(78)$
$Vy = V*sin(78) - gt$
$0 = V*sin(78) - 10t$
$t = \frac{18*sin(78)}{10}$
$Sy = S_0y + V_0y*t - \frac{1}{2} *gt^2$
$h = Sy = 18*sin(78)*( \frac{18*sin(78)}{10} ) - 5*( \frac{18^2*sin^2(78)}{100})$
$h = \frac{3240*sin^2(78)}{100} - \frac{1620*sin^2(78)}{100}$
$h = \frac{81*sin^2(78)}{5}$

Answer 2

Answer:

$h = 15.8 m$

Explanation:

As we know that the velocity of the apple is given as

$v = 18 m/s$ at an angle of 78 degree from horizontal

so here two components of the velocity is given as

$v_x = 18 cos78$

$v_y = 18 sin78$

now as it rises up then due to deceleration of gravity it will slow down and finally comes to rest

so here we can use kinematics to find the maximum height

$v_f^2 - v_i^2 = 2 a h$

$0 - (18sin78)^2 = 2(-9.81)h$

$h = 15.8 m$