A projectile with initial velocity experiences the variable force , where is in .
a. What is the projectile’s speed at s?
b. At what instant of time is the projectile moving parallel to theaxis?
a). The projectile's speed at is .
b). The projectile moving parallel to the axis at .
We are given the force in two dimensions in the form
is the mass of the projectile
Let's find the acceleration for component and :
According to Newton's law, the power exerted on a object creates its accelerates and this force equal to the mass:
Let's compute the final velocity as follow:
For the horizontal component:
For the vertical component:
Place the and values in the given equation:
The projectile's speed at is .
We are given the force in two dimensions in the form.
Let's apply the equation of horizontal component to find the time:
The projectile moving parallel to the axis at .
In the absence of air resistance, a projectile that lands at the CALC elevation from which it was launched achieves maximum range when launched at a 45o angle. Suppose a projectile of mass m is launched with speed v0 into a headwind that exerts a constant, horizontal retarding force
a. Find an expression for the angle at which the range is maximum.
b. By what percentage is the maximum range of a 0.50kg ball reduced if Fwind = 0.60 N ?
A model rocket is on a cart that is rolling to the right at a speed of . The rocket engine, when it is fired, exerts an vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is above the ground. At what horizontal distance left of the hoop should you launch?
In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says “No children under 30 kg allowed.” What is the minimum angular speed, in rpm, for which the ride is safe?
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