APPCM U1 Test Review
𝑜
1. A rocket is launched from a launch pad at an angle of 53 above the horizontal with an initial
2
velocity of 100 𝑚/𝑠. The fuel burns for 3 𝑠 causing a net acceleration of 30 𝑚/𝑠 along the launch
angle. Once the fuel is exhausted, the rocket proceeds in free fall motion until it reaches the
landing position, which is at the same vertical position as the launch pad. (hint: split the
launch into two sections. Let the x-direction be along the path of the acceleration due to
the fuel and let the y-direction be vertial for the free-fall)
a. Determine the maximum height the rocket reaches above the launch pad.
b. Determine the total time it is in flight, from the moment it leaves the launch pad until it
reaches the landing position.
c. Determine the horizontal range, the total distance from the launch pad to the landing
position.
2. A particle moves in the x/y plane according to the position vector given by:
^ 4 2 ^
𝑟(𝑡) = (− 4𝑡) 𝑖 + (2𝑡 − 2𝑡 + 3𝑡) 𝑗
the position is measured in meters.
a. Determine the time at which the particle stops accelerating.
b. Determine the change in position from 𝑡 = 0 to the time the particle stops accelerating (give
your answer in vector notation).
c. Determine the average velocity of the particle from 𝑡 = 0to the time the particle stops
accelerating (give your answer in vector notation).
d. Calculate the velocity of the particle when it stops accelerating (give your answer in vector
notation).
2
3. A particle has an acceleration vector of 𝑎(𝑡) = (4𝑖 + 3𝑗) 𝑚/𝑠 At time zero, the particle is at
𝑥 = 4𝑚 and 𝑦 = 3𝑚 and starts from rest.
a. Determine the velocity (in unit vector notation) at 2 seconds.
b. Determine the position (in unit vector notation) at 2 seconds.
c. Determine the magnitude and direction of the displacement from the origin at 2 seconds.
d. When, if ever, does the particle stop moving?
This study source was downloaded by 100000899606070 from CourseHero.com on 06-17-2025 01:56:24 GMT -05:00
https://www.coursehero.com/file/188775856/21-APPCM-U1-Test-Reviewpdf/
𝑜
1. A rocket is launched from a launch pad at an angle of 53 above the horizontal with an initial
2
velocity of 100 𝑚/𝑠. The fuel burns for 3 𝑠 causing a net acceleration of 30 𝑚/𝑠 along the launch
angle. Once the fuel is exhausted, the rocket proceeds in free fall motion until it reaches the
landing position, which is at the same vertical position as the launch pad. (hint: split the
launch into two sections. Let the x-direction be along the path of the acceleration due to
the fuel and let the y-direction be vertial for the free-fall)
a. Determine the maximum height the rocket reaches above the launch pad.
b. Determine the total time it is in flight, from the moment it leaves the launch pad until it
reaches the landing position.
c. Determine the horizontal range, the total distance from the launch pad to the landing
position.
2. A particle moves in the x/y plane according to the position vector given by:
^ 4 2 ^
𝑟(𝑡) = (− 4𝑡) 𝑖 + (2𝑡 − 2𝑡 + 3𝑡) 𝑗
the position is measured in meters.
a. Determine the time at which the particle stops accelerating.
b. Determine the change in position from 𝑡 = 0 to the time the particle stops accelerating (give
your answer in vector notation).
c. Determine the average velocity of the particle from 𝑡 = 0to the time the particle stops
accelerating (give your answer in vector notation).
d. Calculate the velocity of the particle when it stops accelerating (give your answer in vector
notation).
2
3. A particle has an acceleration vector of 𝑎(𝑡) = (4𝑖 + 3𝑗) 𝑚/𝑠 At time zero, the particle is at
𝑥 = 4𝑚 and 𝑦 = 3𝑚 and starts from rest.
a. Determine the velocity (in unit vector notation) at 2 seconds.
b. Determine the position (in unit vector notation) at 2 seconds.
c. Determine the magnitude and direction of the displacement from the origin at 2 seconds.
d. When, if ever, does the particle stop moving?
This study source was downloaded by 100000899606070 from CourseHero.com on 06-17-2025 01:56:24 GMT -05:00
https://www.coursehero.com/file/188775856/21-APPCM-U1-Test-Reviewpdf/
