A shot putter, launches a $7.260 \mathrm{kg}$ shot by pushing it along a straight line of length $1.650 \mathrm{m}$ at an angle of $34.10°$ from the horizontal, accelerating the shot to the launch speed from its initial speed of $2.500 \mathrm{m} {\mathrm{s}}^{-1}$ (which is due to the athlete's preliminary motion). The shot leaves the hand at a height of $2.110 \mathrm{m}$ at an angle of $34.10°$ and it lands at a horizontal distance of $15.98 \mathrm{m}$. What is the magnitude of the athlete's average force on the shot during the acceleration phase? (Hint: Treat the motion during the acceleration phase as it was along a ramp at the given angle)

When two perpendicular forces $9.0 \mathrm{N}$ (towards positive $x$) and $7.0 \mathrm{N}$ (towards positive $y$) act on a body of mass $6.0 \mathrm{kg}$ what are the $\left(a\right)$ magnitude and $\left(b\right)$ direction of the acceleration of the body?

Two horizontal forces act on a $2.5 \mathrm{kg}$ chopping block that can slide over a frictionless kitchen counter, which lies in an $xy$ plane. One force is ${\overrightarrow{F}}_1=\left(3.0 \mathrm{N}\right)\hat{\mathrm{i}}+\left(4.0 \mathrm{N}\right)\hat{\mathrm{j}}$. Find the acceleration of the chopping block in unit-vector notation when the other force is

$\left(a\right) {\overrightarrow{F}}_2=\left(-3.0 \mathrm{N}\right)\hat{\mathrm{i}}+\left(-4.0 \mathrm{N}\right)\hat{\mathrm{j}}$,

$\left(b\right) {\overrightarrow{F}}_2=\left(-3.0 \mathrm{N}\right)\hat{\mathrm{i}}+\left(4.0 \mathrm{N}\right)\hat{\mathrm{j}}$ and

$\left(c\right) {\overrightarrow{F}}_2=\left(3.0 \mathrm{N}\right)\hat{\mathrm{i}}+\left(-4.0 \mathrm{N}\right)\hat{\mathrm{j}}$

Three astronauts, propelled by jet backpacks, push and guide a $120 \mathrm{kg}$ asteroid towards a processing dock, exerting the forces, as shown in the figure with $F_1=32 \mathrm{N}$, $F_2=55 \mathrm{N}$, $F_3=41 \mathrm{N}$, ${\text{θ}}_1=30°$  and ${\text{θ}}_3=60°$.

What is the asteroid's acceleration

(a) in a unit vector notation?

(b) as a magnitude?

(c) as a direction, relative to the positive direction of the $x$-axis?

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tyre at the angles shown in the overhead view in the figure shown below. The tyre remains stationary in spite of the three pulls. Alex pulls with force ${\overrightarrow{F}}_{\mathrm{A}}$ of magnitude $250 \mathrm{N}$ and Charles pulls with force ${\overrightarrow{F}}_{\mathrm{C}}$ of magnitude $170 \mathrm{N}$. Note that the direction of ${\overrightarrow{F}}_{\mathrm{C}}$ is not given. What is the magnitude of Betty's force ${\overrightarrow{F}}_{\mathrm{B}}?$

There are two forces on the $2.00 \mathrm{kg}$ box in the overhead view of in figure shown below but only one is shown. For $F_1=20.0 \mathrm{N}$ and
$\mathrm{\theta }=30.0°$, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the $x-$axis.