Question

For each of the following textbook problems (ch3) use the projectile motion equation to determine the following. Assume no air resistance. {Be sure to use the appropriate signs to indicate direction}: A golf hall rolls off a horizontal cliff with an initial (horizontal) speed of 11.4 m/s. The ball falls a vertical distance of 15.5 m into a lake below. a. How much time does the ball spend in the air? b. What is the horizontal distance from the cliff at which it strikes the water? c. What arc the horizontal (x) and vertical (y) components of the ball's velocity the instant it strikes the water? v_x = v_y =

Answer 1

Initial speed of golf ball in the horizontal direction is $u_x=11/4\,m/s$

Initial speed of golf ball  in the vertical direction is $u_y=0$

Height of the cliff is $h=15.5\,m$

a)

using $S=ut+\frac{1}{2}at^2$

$h=u_yt+\frac{1}{2}gt^2$

$15.5=(0)t+\frac{1}{2}(9.8)t^2$

$t=1.78\,s$

Time during which the ball is in air is $t=1.78\,s$

b)

Horizontal distance from the cliff at which the ball strikes water is    $x=u_xt$

$x=(11.4)(1.78)=20.3\,m$

c)

using $v^2-u^2=2aS$

$v_x^2-u_x^2=0$    that is $v_x=u_x=11.4\,m/s$

$v_y^2-u_y^2=2gh$    that is $v_y=\sqrt{2gh}=\sqrt{2\times9.8\times15.5}=17.4\,m/s$