## Related questions with answers

A small blimp is used for advertising purposes at a football game. It has a mass of $93.5 \mathrm{~kg}$ and is attached by a towrope to a truck on the ground. The towrope makes an angle of $53.3^{\circ}$ downward from the horizontal, and the blimp hovers at a constant height of $19.5 \mathrm{~m}$ above the ground. The truck moves on a straight line for $840.5 \mathrm{~m}$ on the level surface of the stadium parking lot at a constant velocity of $8.90 \mathrm{~m} / \mathrm{s}$. If the drag coefficient $(K$ in $F=K v^2$ ) is $0.500 \mathrm{~kg} / \mathrm{m}$, how much work is done by the truck in pulling the blimp (assuming there is no wind)?

Solution

VerifiedGiven the following data

$\begin{aligned} m&=93.5\ \mathrm{kg}\\ \theta&=53.3^{\circ}\\ h&=19.5\ \mathrm{m}\\ d&=840.5\ \mathrm{m}\\ v&=8.90\ \mathrm{\dfrac{m}{s}}\\ K&=0.500\ \mathrm{\dfrac{kg}{m}}\\ \end{aligned}$

our objective is to calculate the work $W$ done by the truck when pulling the blip.

We'll do so by applying the formula

$\begin{equation} W=\vec{F}\cdot\vec{d}\end{equation}$

Sketching this problem and analyzing the forces is recommended before doing any calculations.

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