A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked,…

Question

asked Nov 13, 2021 186k views

1 Answer

Sujith Sandeep · Answer 1 · 2021-11-18T19:05:00+0000

Answer:

The difference is height is
$\Delta h =6.92 \ m$

Step-by-step explanation:

From the question we are told that

The distance of ball from the goal is
$d = 36.0 \ m$

The height of the crossbar is
$h = 3.05 \ m$

The speed of the ball is
$v = 21.6 \ m/s$

The angle at which the ball was kicked is
$\theta = 50 ^o$

The height attained by the ball is mathematically represented as

H = v_v * t - (1)/(2) gt^2

Where
v_v is the vertical component of velocity which is mathematically represented as

$v_v = v * sin (\theta )$

substituting values

v_v = 21.6 * (sin (50 ))

$v_v = 16.55 \ m/s$

Now the time taken is evaluated as

$t = (d)/(v * cos(\theta ))$

substituting value

t = (36)/(21.6 * cos(50 ))

$t = 2.593 \ s$

So

H = 16.55 * 2.593 - (1)/(2) * 9.8 * (2.593)^3

$H = 9.97 \ m$

The difference in height is mathematically evaluated as

$\Delta h = H - h$

substituting value

$\Delta h = 9.97 - 3.05$

$\Delta h =6.92 \ m$