A basketball has a mass of 575 g. Moving to the right and heading downward at an angle of 31° to the vertical, it hits the floor with a speed of 4 m/s and bounces up with nearly the same speed, again moving to the right at an angle of 31° to the vertical. What was the momentum change ? (Take the axis to be to the right and the axis to be up. Express your answer in vector form.)

Answers

Answer 1

Answer:

Answer:

Taking the x axis to the right and the y axis to be up, the total change of momentum is $\Delta \vec{ p} = 3.9429 (kg \ m)/(s) \hat{j}$

Explanation:

The momentum $\vec{p}$ is given by:

$\vec{p} = m \ \vec{v}$

where m is the mass and $\vec{v}$ is the velocity. Now, taking the suffix i for the initial condition, and the suffix f for the final condition, the change in momentum will be:

$\Delta \vec{ p} = \vec{p}_f - \vec{p}_i$

$\Delta \vec{ p} = m \ \vec{v}_f - m \ \vec{v}_i$

$\Delta \vec{ p} = m (\ \vec{v}_f - \ \vec{v}_i)$

As we know the mass of the ball, we just need to find the initial and final velocity.

Knowing the magnitude and direction of a vector, we can obtain the Cartesian components with the formula

$\ \vec{A} = | \vec{A} | \ ( \ cos(\theta) \ , \ sin (\theta) \ )$

where $| \vec{A} |$ is the magnitude of the vector and θ is the angle measured from the x axis.

Taking the x axis to the right and the y axis to be up, the initial velocity will be:

$\vec{v}_i = 4 (m)/(s) ( \ cos ( - (90 \ °- 31 \°)) , sin( - (90 \ ° - 31\°) ) ) =$

where minus sign appears cause the ball is going downward, and we subtracted the 31 ° as it was measured from the y axis

So, the initial velocity is

$\vec{v}_i = 4 (m)/(s) ( \ cos ( - 59 \°) , sin( - 59 \°)) =$

$\vec{v}_i = ( \ 2.0601 \ (m)/(s) , - 3.4286 (m)/(s)) =$

The final velocity is

$\vec{v}_i = 4 (m)/(s) ( \ cos ( 90 \ °- 31 \°) , sin( 90 \ ° - 31\°)) =$

$\vec{v}_i = 4 (m)/(s) ( \ cos ( 59 \°) , sin( 59 \°)) =$

$\vec{v}_i = ( \ 2.0601 \ (m)/(s) , 3.4286 (m)/(s)) =$

So, the change in momentum will be

$\Delta \vec{ p} = m (\ \vec{v}_f - \ \vec{v}_i)$

$\Delta \vec{ p} = 0.575 \ kg (\ ( \ 2.0601 \ (m)/(s) , 3.4286 (m)/(s) - ( \ 2.0601 \ (m)/(s) , - 3.4286 (m)/(s)))$

$\Delta \vec{ p} = 0.575 \ kg (\ ( \ 2.0601 \ (m)/(s) - \ 2.0601 \ (m)/(s), 3.4286 (m)/(s) + 3.4286 (m)/(s))$

$\Delta \vec{ p} = 0.575 \ kg (\ 0 , 2 * 3.4286 (m)/(s) )$

$\Delta \vec{ p} = 0.575 \ kg * 2 * 3.4286 (m)/(s) \hat{j}$

$\Delta \vec{ p} = 3.9429 (kg \ m)/(s) \hat{j}$

Related Questions

It's a little hard can u help
Why must the Ojibwe people pay close attention to the seasons? a.) they must be ready to move to a new place where they can hunt b.) they only fish during the warmest times of the day c. they must know the right time of year for Gathering certain foods d.) they still catch walleye with the steering method
Of the four most important pathways by which stress affects health, the first one to occuris usually related to physiology
A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is 9.70 MHz . At this field strength, the Hall voltage on the probe is 0.549 mV when the current through the probe is 0.146 mA . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.735 mV .A) What is the strength of this magnetic field?
A white blood cell has a diameter of approximately 12 micrometers or 0.012 um a model represents its diameter as 24 um what ratio of model size

The animal that is hunted and consumed is considered the

Answers

Predator? like they hunt their prey

Answer:

prey

Explanation:

Shameeka is studying for an exam she took the notable about calcium and chlorine which are known to for my comic born's which shameekas error?

Answers

The individual calcium atom has a positive and not negative, 2 charge

Answer:

The individual calcium atom has a positive, not negative, 2 charge.

Explanation:

Did the quiz also had it on the unit test on edgunity.

Hope this helps guys!

Bailey wants to find out which frozen solid melts the fastest: soda, ice, or orange juice. She pours each of the three liquids into the empty cubes of an ice tray, and then places the ice tray in the freezer overnight. The next day, she pulls the ice tray out and sets each cube on its own plate. She then waits and watches for them to melt. When the last part of the frozen liquid melts, she records the time.

Answers

Answer:

its 45 over 6

Explanation:the answer is in the question

Answer: Only the melted cube's shape changed.

Explanation:

You are given a parallel plate capacitor with plates having a rectangular area of 16.4 cm2 and a separation of 2.2 mm. The space between the plates is filled with a material having a dielectric constant κ = 2.0.Find the capacitance of this system

Answers

Answer: C = 1.319×10^-11 F

Explanation: The formulae that relates the capacitance of a capacitor to the area of the plates, distance between the plates and dielectric constant is given as

C = kε0A/d

Where C = capacitance of plates =?

k = dielectric constant = 2.0

Area of plates = 16.4cm² = 0.00164 m²

d = distance between plates = 2.2 mm = 0.0022m

By substituting the parameters, we have that

C = 2 × 8.85×10 ^-12 ×0.00164/ 0.0022

C = 0.029028 × 10^-12/ 0.0022

C = 13.19× 10^-12

C = 1.319×10^-11 F

1. Two forces F~ 1 and F~ 2 are acting on a block of mass m=1.5 kg. The magnitude of force F~ 1 is 12N and it makes an angle of θ = 37◦ with the horizontal as shown in figure-1. The block is sliding at a constant velocity over a frictionless floor.(a) Find the value of the normal force on the block.

(b) Find the magnitude of force F~2 that is acting on the block

(c) Find the magnitude of force F~ 2 if the block accelerates with a magnitude of a = 2.5 m/s2 along the direction of F~ 2 .

Answers

Answer:

Normal force=7.48 N

Explanation:

N+F~1 sinθ-mg=0

=>N=1.5*9.8-12 sin37◦

=>N=14.7-7.22=7.48 N

wo balls have the same mass of 5.00 kg. Suppose that these two balls are attached to a rigid massless rod of length 2L, where L = 0.550 m. One is attached at one end of the rod and the other at the middle of the rod. If the rod is held by the open end and rotates in a circular motion with angular speed of 45.6 revolutions per second,