kolonelyf4
2021-11-07
Answered

The particle travels along the path defined by the parabola $y=0.5{x}^{2}$ . If the component of velocity along the x axis is vx = (5t) ft/s, where t is in seconds, determine the particle’s distance from the origin O and the magnitude of its acceleration when t = 1 s. When t = 0, x = 0, y = 0.

You can still ask an expert for help

David Tyson

Answered 2021-11-08
Author has **19** answers

From the equation for $v}_{x$ we can get an equation for x:

$x=2.5{t}^{2}$

We can insert that to find the equation for y as a function of time:

$y=0.5\cdot {2.5}^{2}\cdot {t}^{4}=3.125{t}^{4}$

Distance at the t=1 is:

${d}_{x}=2.5$ ft

${d}_{y}=3.125ft$

$d=\sqrt{{d}_{x}+{d}_{y}}=\sqrt{{2.5}^{2}+{3.125}^{2}}$

$d=4$ ft

Acceleration in t=1 is:

$a}_{y}=37.5t=37.5\text{}f\frac{t}{{s}^{2}$

$a}_{x}=5\text{}f\frac{t}{{s}^{2}$

$a=\sqrt{{a}_{x}+{a}_{y}}=\sqrt{{5}^{2}+{37.5}^{2}}$

$a=37.83\text{}f\frac{t}{{s}^{2}}$

Result:$d=4\text{}ft$

$a=37.83\text{}f\frac{t}{{s}^{2}}$

We can insert that to find the equation for y as a function of time:

Distance at the t=1 is:

Acceleration in t=1 is:

Result:

asked 2020-12-28

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and the plane is 0.35.

a) Calculate the acceleration of each block

b) Calculate the tension in the string

c) What happens if the positions of the block are reversed, so that the 4.00-kg block is above the 8.00-kg block?

asked 2020-11-05

A 0.50 kg ball that is tied to the end of a 1.1 m light cord is revolved in a horizontal planewith the cord making a

a) Determine the ball speed.

b) If, instead, the ball is revolved so that its speed is 4.0 m/s,what angle does the cord make with the vertical?

c) If the cord can withstand a maximum tension of 9.1 N, what is the highest speed at which the ballcan move?

asked 2021-02-19

Three Children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and avery light board 3.6 m long. Two playmates are already on either end. Boy A has a mass of 50kg, and girl B a mass of 35 kg. Where should girl C, whose mass is 25 kg, placed herself so as to balance the seesaw.

asked 2021-02-06

A 0.450 kg ice puck, moving east with a speed of $3.00\frac{m}{s}$ has a head in collision with a 0.900 kg puck, initially at rest. Assuming a perfectly elastic collision what will be the speed and direction of each object after the collision?

asked 2021-10-21

Use the two-way table of data from another student survey to answer the following question.

What is the conditional relative frequency that a student likes to lift weights, given that the student does not like aerobics?

asked 2022-01-04

A rock climber stands on top of a 50-m-high cliff overhanging a pool of water. He throws stones vertically downward 1.0 s apart and observes that the cause a single splash. The initial speed of the first stone was 2.0 m/s.

a. How long after the release of the first stone does the second stone hit the water?

b. What was the initial speed of the second stone?

c. What is the speed of each stone as it hits the water?

a. How long after the release of the first stone does the second stone hit the water?

b. What was the initial speed of the second stone?

c. What is the speed of each stone as it hits the water?

asked 2021-01-13

An ice cube tray of negligible mass contains 0.315 kg of water at $17.7}^{\circ$ . How much heat must be removed to cool the water to $0.0}^{\circ$ and freeze it?