1, Ebo through a ball into the air. its velocity at the start is 18m/s at an angle of 37° to the ground.

a, Express the initial velicity in component vector form
b, Work out the velocity of the ball as it lands. give answer in component vector form.
c, Work out the range of the ball.
d, What assumptions have been made about the frame reference?

a.

Vx = 18 cos 37 forever
Vy = 18 sin 37 at start
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b.
assuming it started at ground level the x velocity will be the same but the y velocity will be the same magnitude but down not up
Vx = 18 cos 37 forever
Vy = -18 sin 37 at landing

c.
how long until it lands?
h = Hi + Vi t - 4.9 t^2
Hi = h = 0 at ground
Vi = 18 sin 37
so at the end
0 = 0 + 18 sin 37 * t - 4.9 t^2
(4.9 t - 18 sin 37 ) t = 0
so at the ground = t = 0 and at t = (18/4.9)sin 37
so
x = Vx t = (18 cos 37) (18 sin 37 ) / 4.9

d. well as I said I assumed the ball started at the ground level but the kid probably had finite height. It is an inertial frame, not really earth with its Coriolis effect etc.

18. 9

Biniyam Tefera

a, To express the initial velocity in component vector form, we need to find the horizontal and vertical components.

The horizontal component can be calculated using the equation: Vx = V * cos(θ), where V is the magnitude of the velocity (18 m/s) and θ is the angle to the ground (37°).

Vx = 18 m/s * cos(37°)

The vertical component can be calculated using the equation: Vy = V * sin(θ), where V is the magnitude of the velocity (18 m/s) and θ is the angle to the ground (37°).

Vy = 18 m/s * sin(37°)

Therefore, the initial velocity in component vector form is:
Vx = (18 m/s * cos(37°))i
Vy = (18 m/s * sin(37°))j

b, To calculate the velocity of the ball as it lands, we need to find the vertical component of the velocity at that point. Since the ball lands on the ground, the vertical component of the velocity will be -Vy.

Therefore, the velocity of the ball as it lands in component vector form is:
Vx = (18 m/s * cos(37°))i
Vy = -(18 m/s * sin(37°))j

c, To calculate the range of the ball, we can use the formula: Range = (Vx * 2 * Vy) / g, where g is the acceleration due to gravity (9.8 m/s^2).

Range = (18 m/s * cos(37°) * 2 * (18 m/s * sin(37°))) / 9.8 m/s^2

d, The assumptions made about the frame of reference are that there is no air resistance, the acceleration due to gravity is constant throughout the motion, and there are no external forces acting on the ball during flight. Also, for simplicity, we assume a flat surface and neglect factors like spin and air currents.

Hope that gives you a good laugh along with the answers!

To answer these questions, we'll need to use some basic principles of projectile motion and vector components. Let's go through each question step by step:

a) Express the initial velocity in component vector form:
To express the initial velocity in component vector form, we need to break it down into horizontal and vertical components. We can use the following trigonometric relationships:

Horizontal Component (Vx) = Velocity * cos(angle)
Vertical Component (Vy) = Velocity * sin(angle)

Using the given values:
Velocity = 18 m/s
Angle = 37°

So, the initial velocity in component vector form is:
Vx = 18 * cos(37°)
Vy = 18 * sin(37°)

b) Work out the velocity of the ball as it lands in component vector form:
When the ball lands, its vertical component (Vy) will be zero, as it reaches its maximum height and starts falling back down. The horizontal component (Vx) will remain constant.

To find the time it takes for the ball to land, we can use the equation:
Time = (2 * Vy) / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).

Using the given values:
Vy = 18 * sin(37°)
g = 9.8 m/s²

So, the time it takes for the ball to land is:
Time = (2 * Vy) / g = (2 * 18 * sin(37°)) / 9.8

Once we have the time, we can find the horizontal component (Vx) at that time, which will be the velocity as the ball lands.

Velocity as it lands in component vector form:
Vx = Vx (initial)
Vy = 0

c) Work out the range of the ball:
The range of the ball is the horizontal distance it travels before it lands. We can use the equation for horizontal distance:

Range = Vx * Time

Using the values we calculated earlier:
Range = Vx (initial) * Time

d) Assumptions about the frame of reference:
In this scenario, some assumptions have been made about the frame of reference. These assumptions include:
- Neglecting air resistance: The calculation assumes that there is no air resistance acting on the ball during its flight.
- Uniform gravitational field: The calculation assumes a constant gravitational field with a value of approximately 9.8 m/s².

These assumptions simplify the calculations and make them more realistic for projectile motion in idealized situations.

A brass rod 2m long at a certain temperature.what is it’s length after a temperature rise of 100k if the expansivity of brass is 18x10-6k-1