Question

In: Physics

A particle leaves the origin with an initial velocity of 4.10 m/s in the x direction,...

A particle leaves the origin with an initial velocity of 4.10 m/s in the x direction, and moves with constant acceleration ax = -1.40 m/s2 and ay = 3.80 m/s2. How far does the particle move in the x direction before turning around? What is the particle's velocity at this time? Enter the x component first, followed by the y component.

Expert Solution

Given the initial velocity components


And given the acceleration components


And so, from the kinematical equations, we get for the x component

and

Alternatively, we get

And for the particle to turn around in the x-direction, we require the particle velocity to become zero momentarily, i.e.,



And so, putting the given values, we get


And the time at which the particle turn around in the x direction, is given by


So, putting the given values, we get


The velocity at this time along the x direction is zero, i.e,

The motion in the y direction is given by

So, at the above time, we get the velocity in the y direction

genius_generous answered 7 months ago

A particle leaves the origin with initial velocity v⃗ =15i^+18j^m/s v→o=15i^+18j^m/s, undergoing constant acceleration a⃗ =−1.5i^+0.31j^m/s2a→=−1.5i^+0.31j^m/s2....

A particle leaves the origin with initial velocity v⃗ =15i^+18j^m/s v→o=15i^+18j^m/s, undergoing constant acceleration a⃗ =−1.5i^+0.31j^m/s2a→=−1.5i^+0.31j^m/s2. in what direction is it moving ?

Particle A of mass m, initial velocity 20i (m/s) has a collision with a stationary particle...

Particle A of mass m, initial velocity 20i (m/s) has a collision with a stationary particle B of mass 2m. After collision, VA(final)=10i+5j (m/s). a) Find VB(final) if the system (particle A plus B) linear momentum is conserved (both i and j directions). What are the velocities of center of the system before and after collision?b) Find the system’s % KE lost due to the collision (m=20.0gram). c) If the collision time between A and B is 0.050 s, what...

ball is kicked with an initial velocity of 21 m/s in the horizontal direction and 13...

ball is kicked with an initial velocity of 21 m/s in the horizontal direction and 13 m/s in the vertical direction. (Assume the ball is kicked from the ground.) (a) At what speed (in m/s) does the ball hit the ground? m/s (b) For how long (in s) does the ball remain in the air? s (c) What maximum height (in m) is attained by the ball? m

A proton has an initial velocity of 7.6 × 106 m/s in the horizontal direction. It...

A proton has an initial velocity of 7.6 × 106 m/s in the horizontal direction. It enters a uniform electric field of 8800 N/C directed vertically. a) Ignoring gravitational effects, find the time it takes the proton to travel 0.127 m horizontally. The mass of the proton is 1.6726 × 10−27 kg and the fundamental charge is 1.602 × 10−19 C . Answer in units of ns. b)What is the vertical displacement of the proton after the electric field acts...

A block of 4 kg moves in the +x direction with a velocity of 15 m/s...

A block of 4 kg moves in the +x direction with a velocity of 15 m/s while a block of 6 kg moves in the +y direction with a velocity of 10 m/s. They collide and stick together. Calculate the following: a. What is the momentum in this system? b. What is the final velocity of the two blocks?

Particle A (mA = 1 kg) is given initial velocity 10 m/s to the right, while...

Particle A (mA = 1 kg) is given initial velocity 10 m/s to the right, while particle B (mB = 1:5 kg) is initially at rest. The coecient of restitution for any impact between A and B is 2/3 while the coecient of restitution for impact of either particle with either wall is 5/6. The particles slide along a smooth horizontal supporting surface. Compute the percentage of the kinetic energy remaining in the system of A and B at the...

Billiard ball A of mass 1.00 kg is given a velocity 7.10 m/s in +x direction...

Billiard ball A of mass 1.00 kg is given a velocity 7.10 m/s in +x direction as shown in the figure. Ball A strikes ball B of the same mass, which is at rest, such that after the impact they move at angles ΘA = 63.0 ° and ΘB respectively. The velocity of ball A after impact is 4.20 m/s in the direction indicated in the figure. Figure showing a layout of the problem as described in text. A) What...

off a cliff 100.0 m high with a velocity of 15.0 m/s. (a) Define the origin...

off a cliff 100.0 m high with a velocity of 15.0 m/s. (a) Define the origin of the coordinate system. (b) Which equation describes the horizontal motion? (c) Which equations describe the vertical motion? (d) What is the rock’s velocity at the point of impact?

An object is launched at a velocity of 20 m/s in a direction making an angle...

An object is launched at a velocity of 20 m/s in a direction making an angle of 25 degrees upward with the horizontal. a) What is the maximum height reached by the object? b) What is the total flight time (between launch and touching the ground) of the object? c) What is the horizontal range (maximum x above ground) of the object? d) What is the magnitude of the horizontal component of the velocity of the object just before it...

A charged particle of mass m = 7.3X10-8 kg, moving with constant velocity in the y-direction...

A charged particle of mass m = 7.3X10-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 1.8T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.5 m, 0) and leaves the region at (x,y) = 0, 0.5 m a time t = 463 μs after it entered the region. 1. With what speed v did the particle enter the region containing the magnetic...