The punter stands on the 22 yard (roughly a meter) line to the left of the 50 yard line and the ball is kicked with an initial velocity of 25.3 m/s at an angle of 58.5° above the ground. Where does the ball land?

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The punter stands on the 22 yard (roughly a meter) line to the left of the 50 yard line and the ball is kicked with an initial velocity of 25.3 m/s at an angle of 58.5° above the ground. Where does the ball land?

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Answer 1 · 2015-09-26T00:58:32

The ball will land at approximately the $14$ $14$ yard line on the opposite side of the field.

Explanation:

launch angle: ${58.5}^{o}$ $58.5^"o"$
initial velocity: $v_{i} = 25.3 m/s$ $v_i=25.3"m/s"$

Vertical Motion Required to Find Time

initial vertical velocity: $v_{iy} = 25.3 m/s \cdot {sin 58.5}^{o} = 21.6 m/s$ $v_"iy"=25.3"m/s"*sin58.5^"o"=21.6"m/s"$

final vertical velocity: $- 21.6 m/s$ $-21.6"m/s"$

time:
$v_{fy} = v_{iy} + gt$ $v_"fy"=v_"iy" + "gt"$

$- 21.6 m/s = 21.6 m/s + (- 9.81 {m/s}^{2}) t$ $-21.6"m/s"=21.6"m/s"+(-9.81"m/s"^2)t$

$- 43.2 m/s = (- 9.81 {m/s}^{2}) t$ $-43.2"m/s"=(-9.81"m/s"^2)t$

$\frac{- 43.2 m/s}{- 9.8 {m/s}^{2}} = t$ $(-43.2"m/s")/(-9.8"m/s"^2)=t$

$t = 4.40 s$ $t=4.40"s"$

Horizontal Motion

initial horizontal velocity: $v_{ix} = 25.3 m/s \cdot {cos 58.5}^{o} = 13.2 m/s$ $v_"ix"=25.3"m/s"*cos58.5^"o"=13.2"m/s"$

range: $x = x_{ix} \cdot t = 13.2 m/s \cdot 4.40 s = 58.1 m$ $x=x_"ix"*t=13.2"m/s"*4.40"s"=58.1"m"$

Because an American football field is marked in yards, convert $58.1 m$ $58.1"m"$ to yards.

$58.1 m \times \frac{1.094 yd}{1 m} = 63.6 \approx 64 yards$ $58.1"m"xx(1.094"yd")/(1"m")=63.6~~64"yards"$

The ball started out on the $22$ $22$ yard line and traveled an additional $64$ $64$ yards. An American football field is $100$ $100$ yards in length. The $50$ $50$ yard line is in the center.

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The location of the ball at the end of its flight will be $(50 - 22) - (50 - 36) = 14$ $(50-22)-(50-36)=14$

The ball will land at approximately the $14$ $14$ yard line on the other side of the $50$ $50$ yard line.

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The punter stands on the 22 yard (roughly a meter) line to the left of the 50 yard line and the ball is kicked with an initial velocity of 25.3 m/s at an angle of 58.5° above the ground. Where does the ball land?

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Explanation:

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