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Solution to DYNAMICS (ENGR_212_400_S2018) Assignment #1

**Problem #1:**

Problem #1, Part a:

Determine the time (in seconds) required for a train to travel 1 [km] along its rails if the train starts from rest, reaches a maximum speed at some intermediate point, and then stops at the end of the road. The train can accelerate at 1.5 [m/(sˆ2)] and decelerate at 2 [m/(sˆ2)].

Problem #1, Part b:

The acceleration of a asteroid traveling a straight line is a=(1/4)s^(1/2)[m/(sˆ2)], where s is in meters. If v = 0 [m/s], s= 1 [m] when t = 0 seconds, determine the particle’s velocity (in [m/s]) at s = 2 [m].

**Problem #2:**

Problem #2 Part a:

A train travels along a straight route with an acceleration-deceleration described by Figure1. If the train starts from rest, determine the distance, s’, the car travels until it stops. Construct the v–s graph (in terms of ft/s and feet) for 0≤s≤s’. Construct the graph by hand, but be sure to label it appropriately.

Problem #2 Part b:

A man riding upward in a freight elevator accidentally drops a package oﬀ the elevator when it is 100 feet from the ground. If the elevator maintains a constant upward speed of 4 [ft/s], determine how high (in feet) the elevator is from the ground the instant the package hits the ground. Draw the v–t curve (in terms of ft/s and seconds) for the package during the time it is in motion. Assume that the package was released with the same upward speed as the elevator.

**Problem #3**

Problem #3 Part a:

The van travels over the hill described by [ft]; see Figure2. If it has a constant speed of 75 [ft/s], determine the x and y components of the van’s velocity and acceleration when x = 50 [ft].

Problem #3 Part b:

The motorcycle travels with constant speed along the path that, for a short distance, takes the form of a sine curve; see Figure3. Determine the x and y components of its velocity at any instant on the curve.**Problem #4:**

A projectile is given a velocity ; see Figure4. Determine the angle, (in radians), at which it should be launched so that, d, is a maximum. The acceleration due to gravity is g.

**Problem #5:**

The baseball player A hits the baseball at and from the horizontal. When the ball is directly overhead of player B he begins to run under it; see Figure5. Determine the constant speed (in [ft/s]) at which B must run and the distance d (in feet) in order to make the catch at the same elevation at which that ball was hit.

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