1. Your big brother, despite warning, drops a penny off the observation deck of the Empire State Building in New York City. The observation
deck is 381 m above the ground. What is the terminal velocity of the
penny? How far has the penny fallen after 3 seconds?

The marble will take 8.813 seconds to hit the ground.

Explanation:

The marble will fall according to this motion equation: y(final) = y(initial) + v(initial)×t + 1/2×a×t×t

y(final)=0 m, the marble's final position in relation to the ground

y(initial)=381 m, the marble's initial position in relation to the ground

v(initial)=0 m/s (meters per second), the marble's initial velocity (speed with direction) when fall first begins

t=? seconds, this is the amount of time that passes while falling, the variable in this problem

a=-9.81 m/s/s, the rate at which the velocity of the marble changes, acceleration. On Earth, neglecting friction, acceleration is a constant at negative 9.81 meters per second squared

Plug the values into the equation: 0= 381 + 0t + 1/2(-9.81)(t)(t)

Subtract 381 from both sides and disregard 0t because it has no value and no longer matters: -381= 1/2(-9.81)(t)(t)

Multiply out the equation: -381= -4.905(t)(t)

Divide both sides by -4.905 to isolate the variable: 77.676=(t)(t)

Find the square root of both sides: t=8.813 seconds

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards