1.A projectile starts at the coordinate origin and its initial velocity vector makes an angle of 30° with the horizontal. At the instant when the projectile is at the highest point of its trajectory, the position, velocity and acceleration vectors are r, v and a. Which statement is true? A. ris parallel to v B. v is parallel to a C.ris perpendicular to v v is perpendicular to a 2.When a 1 N force acts on an object that has a mass of 1 kg and is able to move freely, the object receives... A. a speed of 1 ms, B. a velocity of 0.102 ms, C. acceleration of 1 ms2 D.an acceleration of 9,8 ms 3.When the velocity of a moving object is doubled, its A. B. C. D. acceleration is doubled momentum is doubled, kinetic energy is doubled potential energy is doubled 4.An elastic collision conserves A. kinetic energy but not momentum, B. momentum but not kinetic energy, C. both momentum and kinetic energy, D. either momentum or kinetic energy 5.The mass of the Earth is about 80 times greater than the mass of the Moon. Assume the Moon orbits around the Earth along an almost circular orbit whose radius is about 60 times the Earth\'s radius. The centre of mass of the Earth-Moon system is located A. within the Earth. B. midway between the Earth and the Moon. C. one quarter of the distance from the Earth out to the Moon. D. three quarters of the distance from the Earth out to the Moon.
Solution
(1) At the highest point of the trajectory, the projectile will have only horizontal component of velocity.
And the acceleration on the projectile is gravitational acceleration which acts in the vertically downward direction.
So, the angle between \'v\' and \'a\' is 90 deg.
Hence, option (D) is the correct answer.
(2) Acceleration, a = F / m = 1 / 1 = 1.0 m/s^2
Hence, option (C) is the correct answer.
(3) Momentum, Pi = m*v
When velocity is doubled, vf = 2v
So, Pf = m*vf = m*2v = 2*mv = 2*Pi
Hence, option (B) is the correct answer.
(4) Elastic collision conserves both energy and momentum.
Hence, option (C) is the correct answer.
(5) Mass of moon = m
So, mass of the earth = 80m
Radius of the earth = R
So, radius of moon\'s orbit = 60R
So, center of mass of earh-moon system = (m*60R + 0) / (m + 80m) = 0.74R
So, the center of mass is within the earth.
Hence option (A) is the correct answer.
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1-A projectile starts at the coordinate origin and its initial velocit.docx
1. 1.A projectile starts at the coordinate origin and its initial velocity vector makes an angle of 30°
with the horizontal. At the instant when the projectile is at the highest point of its trajectory, the
position, velocity and acceleration vectors are r, v and a. Which statement is true? A. ris parallel
to v B. v is parallel to a C.ris perpendicular to v v is perpendicular to a 2.When a 1 N force acts
on an object that has a mass of 1 kg and is able to move freely, the object receives... A. a speed
of 1 ms, B. a velocity of 0.102 ms, C. acceleration of 1 ms2 D.an acceleration of 9,8 ms 3.When
the velocity of a moving object is doubled, its A. B. C. D. acceleration is doubled momentum is
doubled, kinetic energy is doubled potential energy is doubled 4.An elastic collision conserves
A. kinetic energy but not momentum, B. momentum but not kinetic energy, C. both momentum
and kinetic energy, D. either momentum or kinetic energy 5.The mass of the Earth is about 80
times greater than the mass of the Moon. Assume the Moon orbits around the Earth along an
almost circular orbit whose radius is about 60 times the Earth's radius. The centre of mass of the
Earth-Moon system is located A. within the Earth. B. midway between the Earth and the Moon.
C. one quarter of the distance from the Earth out to the Moon. D. three quarters of the distance
from the Earth out to the Moon.
Solution
(1) At the highest point of the trajectory, the projectile will have only horizontal component of
velocity.
And the acceleration on the projectile is gravitational acceleration which acts in the vertically
downward direction.
So, the angle between 'v' and 'a' is 90 deg.
Hence, option (D) is the correct answer.
(2) Acceleration, a = F / m = 1 / 1 = 1.0 m/s^2
Hence, option (C) is the correct answer.
(3) Momentum, Pi = m*v
When velocity is doubled, vf = 2v
2. So, Pf = m*vf = m*2v = 2*mv = 2*Pi
Hence, option (B) is the correct answer.
(4) Elastic collision conserves both energy and momentum.
Hence, option (C) is the correct answer.
(5) Mass of moon = m
So, mass of the earth = 80m
Radius of the earth = R
So, radius of moon's orbit = 60R
So, center of mass of earh-moon system = (m*60R + 0) / (m + 80m) = 0.74R
So, the center of mass is within the earth.
Hence option (A) is the correct answer.
