When it is 145 m above the ground, a rocket traveling...

When it is 145 $\mathrm{m}$ above the ground, a rocket traveling vertìcally upward at a constant 8.50 $\mathrm{m} / \mathrm{s}$ relative to the ground launches a secondary rocket at a speed of 12.0 $\mathrm{m} / \mathrm{s}$ at an angle of $53.0^{\circ}$ above the horizontal, both quantities being measured by an astronaut sitting in the rocket. Air resistance is too small to worry about. (a) Just as the secondary rocket is lunched, what are the horizontal and vertical components of its velocity relative to (i) the astronaut sitting in the rocket and (ii) Mission Control on the ground? (b) Find the initial speed and launch angle of the secondary rocket as measured by Mission Control. (c) What maximum height above the ground does the secondary rocket reach?

Key Concepts

Vector Components

Decomposing a vector into horizontal and vertical components is essential for solving problems in projectile motion. By breaking the initial velocity into its perpendicular components using trigonometric functions, one can independently analyze the motion in each direction, which simplifies the use of kinematic equations and helps in understanding the overall trajectory.

Relative Velocity

This concept involves understanding how the velocity of one object appears different when measured from different moving reference frames. When an object is launched from a moving platform, its velocity relative to that platform must be combined with the platform's velocity to find the object's velocity as seen by a stationary observer, which is central to problems involving moving observers.

Reference Frame Transformations

This concept deals with translating observations from one frame of reference to another, such as from a moving rocket to a stationary ground-based observer. It requires performing vector addition of velocities measured in different frames and is key when assessing how different observers perceive speeds and directions.

Projectile Motion Kinematics

Projectile motion involves analyzing an object’s motion under the influence of gravity, typically assuming no air resistance. Using kinematic equations allows for calculating various parameters such as maximum height, time of flight, and range, by taking into account the effects of constant acceleration due to gravity on the vertical component of the object's motion.

Transcript

00:01 Hi everyone here it is given when it is 145 meter above the ground.

00:08 A rocket traveling vertically upward at constant speed of 8 .5 meter per second relative to the ground.

00:18 Launch a second rocket at 12 meter per second and 53 degrees above it.

00:26 So second rocket is to be launched with speed v0 2v.

00:36 12 meter per second and alpha knot to be 53 degree.

00:49 If we neglect the air resistance, first we have to calculate what are horizontal and vertical velocity of second rocket.

01:13 First with respect to astronaut sitting in the rocket one in rocket one.

01:45 Second part, mission control on the ground.

02:11 We have to find initial launch angle alpha of secondary rocket as measured by mission control on the ground, sea part.

02:53 What maximum height, the ground, the secondary rocket reach maximum height of r2.

03:06 Let us start solving it with assumptions that considering vertically upward to be positive and right to be positive x -axis after launching of second rocket r to second rocket after launching second rocket it has a x to be zero and a y skull to minus g relative to ground now in the part a velocity of second rocket in horizontal direction 12 cost of 53 7 .72 meter per second and velocity of second rocket along by axis will be 12 sine of 53 that is 9 .58 meter per second second part.

05:24 Velacity of rocket, that is first rocket, with respect to ground along x -axis is 0.

05:38 And velocity of first rocket with respect to ground along by axis is 8 .5 meter per second...

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