All categories

2 years ago

A baseball is thrown with an initial velocity of 45.4 m/s at an angle of 31.2 ∘ .

Physics

1 answer:

sveticcg [70]2 years ago

8 0

Answer:

V (initial vertical velocity) = 45.4 sin 31.2 = 23.52 m/s

1/2 m V^2 = m g h conservation of energy

h = V^2 / (2 g) = 23.52^2 / 19.6 = 28.2 m max height

Check:

t = 28.2 / 9.8 = 2.88 sec time to reach max height

h = 23.52 * 2.88 - 1/2 g 2.88^2 = 27.1 m

You might be interested in

A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straig

inna [77]

Answer:

$\mu_s=\frac{1}{3}\tan \theta$

Explanation:

Let the minimum coefficient of static friction be $\mu_s$ .

Given:

Mass of the cylinder = $M$

Radius of the cylinder = $R$

Length of the cylinder = $L$

Angle of inclination = $\theta$

Initial velocity of the cylinder (Released from rest) = 0

Since, the cylinder is translating and rolling down the incline, it has both translational and rotational motion. So, we need to consider the effect of moment of Inertia also.

We know that, for a rolling object, torque acting on it is given as the product of moment of inertia and its angular acceleration. So,

$\tau =I\alpha$

Now, angular acceleration is given as:

$\alpha = \frac{a}{R}\\Where, a\rightarrow \textrm{linear acceleration of the cylinder}$

Also, moment of inertia for a cylinder is given as:

$I=\frac{MR^2}{2}$

Therefore, the torque acting on the cylinder can be rewritten as:

$\tau = \frac{MR^2}{2}\times \frac{a}{R}=\frac{MRa}{2}------ 1$

Consider the free body diagram of the cylinder on the incline. The forces acting along the incline are $mg\sin \theta\ and\ f$ . The net force acting along the incline is given as:

$F_{net}=Mg\sin \theta-f\\But,\ f=\mu_s N\\So, F_{net}=Mg\sin \theta -\mu_s N-------- 2$

Now, consider the forces acting perpendicular to the incline. As there is no motion in the perpendicular direction, net force is zero.

So, $N=Mg\cos \theta$

Plugging in $N=Mg\cos \theta$ in equation (2), we get

$F_{net}=Mg\sin \theta -\mu_s Mg\cos \theta\\F_{net}=Mg(\sin \theta-\mu_s \cos \theta)--------------3$

Now, as per Newton's second law,

$F_{net}=Ma\\Mg(\sin \theta-\mu_s \cos \theta)=Ma\\\therefore a=g(\sin \theta-\mu_s \cos \theta)------4$

Now, torque acting on the cylinder is provided by the frictional force and is given as the product of frictional force and radius of the cylinder.

$\tau=fR\\\frac{MRa}{2}=\mu_sMg\cos \theta\times R\\\\a=2\times \mu_sg\cos \theta\\\\But, a=g(\sin \theta-\mu_s \cos \theta)\\\\\therefore g(\sin \theta-\mu_s \cos \theta)=2\times \mu_sg\cos \theta\\\\\sin \theta-\mu_s \cos \theta=2\mu_s\cos \theta\\\\\sin \theta=2\mu_s\cos \theta+\mu_s\cos \theta\\\\\sin \theta=3\mu_s \cos \theta\\\\\mu_s=\frac{\sin \theta}{3\cos \theta}\\\\\mu_s=\frac{1}{3}\tan \theta............(\because \frac{\sin \theta}{\cos \theta}=\tan \theta)$

Therefore, the minimum coefficient of static friction needed for the cylinder to roll down without slipping is given as:

$\mu_s=\frac{1}{3}\tan \theta$

3 0

3 years ago

Read 2 more answers

Blank is how high or low you think a sound is

vfiekz [6]

<span>The word is "pitch", which is exactly that: How "high" or "low" a sound is.</span>

3 0

4 years ago

Read 2 more answers

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kow [346]

Answer:

1.122 m/s

Explanation:

So usually a river with a speed of 1 meters per second can transport particle that weighs:

$1^6 = 1 kg$

If the particle is twice as massive as usual, then its weights would be 1 * 2 = 2kg

This means the river must be flowing at a speed of

$2^{\frac{1}{6}} = 1.122 m/s$

5 0

3 years ago

A company is creating a new mosquito repellent, and needs to figure out how much is needed to stop mosquito bites. They find vol

Jlenok [28]

The independent variable is the different amount of repellent each person is given. This is because it does not depend on any variable. The dependent variable is what they are measuring, which would be the number of bites on each volunteer.
I hope this helps! :)

3 0

1 year ago

Objects 1 and 2 attract each other with a electrostatic force of 36.0 units. If the charge of Object 1 is doubled AND the distan

melamori03 [73]

Answer:

8 units

Explanation:

F=(k*q1*q2)/(r^2)

K is a constant, q1 is charge of 1, q2 is charge of 2, r is distance between the two.

6 0

3 years ago