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(a) A daredevil is attempting to run his motorcycle end a line of buses parked end to finish by driving up a 32º ramp in ~ a rate of 40.0 m/s (144 km/h) . How countless buses can he clean if the top of the takeoff ramp is in ~ the same elevation as the bus tops and the buses room 20.0 m long? (b) comment on what your answer implies around the margin the error in this act—that is, take into consideration how much greater the variety is 보다 the horizontal street he have to travel to miss the end of the last bus. (Neglect wait resistance.)
To show the problem, consider the following figure:
The projectile course of the daronger from the ramp
To determine the number of buses that the daredevil deserve to clear, we will divide the variety of the projectile route by 20 m, the size of 1 bus. The is
\beginalign*\textRange & =\frac\textv_\texto^2\:\sin 2\theta \textg \\\textRange & =\frac\left(40.0\:\textm/s\right)^2\sin \left<2\left(32^\circ \right)\right>9.81\:\textm/s^2 \\\textRange & =146.7\:\textm \\\endalign*
\beginalign*\textno. Of buses & =\frac146.7\:\textm20\:\textm \\\textno. The buses & =7.34\:\textbuses \\\textno. That buses & =7\:\textbuses\qquad \qquad\colorDarkOrange \left( \textAnswer \right) \\\endalign*
Therefore, he have the right to only clean 7 buses.
He gets rid of the critical bus through 6.7 m, which seems to be a big margin of error, but because we neglected air resistance, it yes, really isn’t that much room for error.
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