Question

Homework 3

As you know very well from physics, if you hit a ball forward with
a certain angle and a certain speed, it makes an orbital
movement.

The height of the ball is determined by the equation given
below.

y(t)=y_0+v_y0 t-1/2 gt^2

Where y0 is the first location of the ball, vy0 is the initial
vertical velocity of the ball and g is the gravitational
acceleration.

After the ball is thrown, the horizontal distance is determined by
the following equation.

x(t)=x_0+v_x0 t

If the ball is thrown at an angle θ relative to the earth and with
an initial velocity v0, the horizontal and vertical initial
components of the velocity are as follows:

v_x0=v_0 cosθ

v_y0=v_0 sinθ

The flight time of the ball is equal to the following
equation.

t_flight=(2 v_y0)/g

Write a function that determines the trajectory of the ball for
given initial velocity, thrown angle, initial horizontal and
vertical location of the ball. Sample input will be v0=20m/s,
x0=y0=0, θ=[10,80] and Δθ=10°.

Plot the trajectories of this ball and write the formatted output
of the range of the ball against thrown angle to a file called
“range_of_the_ball.txt”.

Write the formatted maximum range of the ball to a file called
“range_of_the_ball.txt”.

can you please solve this on matlab?

Answer #1

A ball is thrown with an initial speed vi at an angle θi with
the horizontal. The horizontal range of the ball is R, and the ball
reaches a maximum height R/8. In terms of R and g, find the
following.
(a) the time interval during which the ball is in motion t =
(b) the ball's speed at the peak of its path v =
(c) the initial vertical component of its velocity yi =
(d)...

2. (15pts, 5pts
each) A ball is thrown from the top of a building that is
H = 40 m height. It has an initial velocity
v0 that is at angle
of = 53° below the horizontal direction, as shown in the
below Figure. The ball hits the ground t = 2.0 s after being
thrown. You may neglect air resistance.
a) Find the magnitude of the initial velocity
v0 of the ball.
b) Find the velocity of the ball just...

3) A ball is thrown leftward from the left edge
of a roof at height “h” above the ground. The ball hits the ground
1.5 sec later at a distance d = 25 m from the building and at an
angle θ = 60° with the horizontal.
a)
What is the value of “h”?
b)
What is the magnitude of the initial velocity?
c)
What is the angle of the initial velocity?

A
ball is thrown from the roof of a building. The initial velocity
vector is at an angle of 53.0° above the horizontal. It is at
maximum height in 1.04 seconds. Express all vectors in terms of
unit vectors i and j. The ball strikes the ground at a horizontal
distance from the building of 33.1 meters.
a.) What is the vertical velocity (vector) at t=1.04
seconds?
b.) What is the initial vertical velocity (vector)?
c) What is the inital...

Suppose the ball is thrown from the same height as in the
PRACTICE IT problem at an angle of 27.0°below the horizontal. If it
strikes the ground 56.3 m away, find the following. (Hint:
For part (a), use the equation for the x-displacement to
eliminate v0t from the equation for
the y-displacement.) horizontal range (height) = 88.64
m
(a) the time of flight = _____s
(b) the initial speed = _____ m/s
(c) the speed and angle of the velocity...

A student throws a water balloon with speed
v0 from a height h = 1.64 m at an
angle θ = 29° above the horizontal toward a target on the
ground. The target is located a horizontal distance d =
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without air resistance. Use a Cartesian coordinate system with the
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Part (a) What is the position vector,
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