Numeracy applications assessment with given formulas

$1$

A con was resting on a book$/$palm$.$ The book$/$palm was lifted upward from rest at $0\mathrm{.}3\frac{m}{s}\frac{?}{s}$ for $0\mathrm{.}2$ second and the stopped at chest level. Find the max height reached by the coin, measured from the chest level., Formulas say that $a=\frac{vf-v0}{t2-t1},a=d\frac{v}{d}t.$ distance $=v{0}^{**}t+a^{**}t$ t t initial distance, vf $=v0+a^{**}t,v{f}^2=v0v^2+2^{**}{a}^{**}$ distance

$2$

There was a swinging pendulum. Find the max height of the bob when the bob had $1\mathrm{.}5\frac{m}{s}$ maximum speed at the minimum height position called position$-$A$.$ What would be the speed of the bob at the maximum height position? $.$Formulas say that $KE={0\mathrm{.}5}^{**}{m}^{**}{v}^{**}v,PE=m^{**}{9\mathrm{.}8}^{**}h$

The string was cut when the bob was at the max height position, find the time for the falling bob to reach position$-$A

The string was cut when the bob was at the minimum height position, Find the fallen distance $0\mathrm{.}001$ second after the cut.

Find the range of the bob when the fallen time to reach ground $=1\mathrm{.}5$ seconds

Was the mass included in any of the equations that you used?

If the mass of the bob was double, would that change the answers above?

$3$

A $3-$kg stone was hurled around moving in a circle by an astronaut in Space with a $2-$meter string attachment. The radial acceleration was $0\mathrm{.}5\frac{m}{s}\frac{?}{s}.$ Find the forces on the stone. Find the fly$-$off speed

Formulas say that $a=v^{**}\frac{v}{R},F=m**a,F=m^{**}d\frac{v}{d}t$

$4$

In daily examples of forces like pushing a box, static friction would be overcome in the initial pushing force to start from rest and the smaller kinetic friction could be overcome with a smaller pushing force to keep going. Formulas say that friction $=$ coefficient$*$Support force

Find the initial pushing force if the static friction coefficient was $0\mathrm{.}35$ for a $50-kg$ box on a flat floor $($PH$201/301/421$ Students: Find the initial pushing force if the static friction coefficient was $0\mathrm{.}35$ for a $50-$kg box on an inclined floor of $30$ degrees, knowing that $sin30=0\mathrm{.}5$ and $cos30=0\mathrm{.}866$

After starting the motion, the pushing force was reduced by $10\%($at $90\%$ level of the initial pushing force$).$ Find the net force on the box when the kinetic friction coefficient was $0\mathrm{.}25.$

After $5$ sec $,$ the engineering situation required a constant speed, find the new pushing force.

$5$

Impulse pair in collision, that is an example of Newton's third law on two interacting objects. A $4$ kg moving at $+5\frac{m}{s}$ collided with a $2$ kg object at $-10\frac{m}{s}.=$

The exchange impulse was $40$ N $-$sec magnitude and opposite directions.

Find the velocity of the $4-$ kg object and $2$ kg object after collision.

Formulas say that $m^{**}vf-m^{**}v0=F^{**}$ contact time

$6$

A $10,000kg$ and $5$ cubic$-$meter object was sitting on a floor. Find the support force of the floor. Formulas say that $F-$net$=m**a$

A $10,000kg$ and $5$ cubic$-$meter object was submerged in a fluid of density of $800$ kg per cubic meter. Find the support force of the fluid using the buoyance force formula of fluid density$*{9\mathrm{.}8}^{**}$ displaced volume