Question

question 22 of 25
you wad up a piece of paper and throw it into the wastebasket. how far will your piece of paper travel if you throw it with a velocity of 3.1 m/s at an angle of 32°? (assume no air resistance and that the paper lands at the same height you threw it from.)
a. 1.1 m
b. 1.6 m
c. 1.3 m
d. 0.88 m

Explanation:

Step1: Identify the range formula

The range formula for projectile motion when the starting and ending heights are the same and there is no air - resistance is $R=\frac{v^{2}\sin2\theta}{g}$, where $v$ is the initial velocity, $\theta$ is the launch angle, and $g = 9.8\ m/s^{2}$ is the acceleration due to gravity.

Step2: Calculate $\sin2\theta$

Given $\theta = 32^{\circ}$, then $2\theta=64^{\circ}$, and $\sin2\theta=\sin64^{\circ}\approx0.8988$.

Step3: Substitute values into the formula

$v = 3.1\ m/s$, so $v^{2}=(3.1)^{2}=9.61\ m^{2}/s^{2}$. Then $R=\frac{9.61\times0.8988}{9.8}$.

Step4: Calculate the range

$R=\frac{9.61\times0.8988}{9.8}=\frac{8.637468}{9.8}\approx0.88\ m$.

Answer:

D. $0.88\ m$