Physics, 12.10.2019 01:20 SoccerHalo

One strategy in a snowball fight is to throw
a snowball at a high angle over level ground.
while your opponent is watching this first
snowball, you throw a second snowball at a
low angle and time it to arrive at the same
time as the first.
assume both snowballs are thrown with
the same initial speed 11.1 m/s. the first
snowball is thrown at an angle of 67◦
above
the horizontal. at what angle should you
throw the second snowball to make it hit the
same point as the first? the acceleration of
gravity is 9.8 m/s
2
.
answer in units of ◦
.
007 (part 2 of 2) 10.0 points
how many seconds after the first snowball
should you throw the second so that they
arrive on target at the same time?
answer in units of s.

Answers: 1

Show answers

Answers

Answer from: NijaNij

Answers:

a) $\theta_{2}=23\°$

b) t=1.199 s

Explanation:

This situation is a good example of the projectile motion or parabolic motion, in which the travel of the snowball has two components: x-component and y-component. Being their main equations as follows for both snowballs:

Snowball 1:

x-component:

$x=V_{o}cos\theta_{1} t_{1}$ (1)

Where:

$V_{o}=11.1 m/s$ is the initial speed of snowball 1 (and snowball 2, as well)

$\theta_{1}=67\°$ is the angle for snowball 1

$t_{1}$ is the time since the snowball 1 is thrown until it hits the opponent

y-component:

$y=y_{o}+V_{o}sin\theta_{1} t_{1}+\frac{gt_{1}^{2}}{2}$ (2)

Where:

$y_{o}=0$ is the initial height of the snowball 1 (assuming that both people are only on the x axis of the frame of reference, therefore the value of the position in the y-component is zero.)

y=0 is the final height of the snowball 1

$g=-9.8m/s^{2}$ is the acceleration due gravity (always directed downwards)

Snowball 2:

x-component:

$x=V_{o}cos\theta_{2} t_{2}$ (3)

Where:

$\theta_{2}$ is the angle for snowball 2

$t_{2}$ is the time since the snowball 2 is thrown until it hits the opponent

y-component:

$y=y_{o}+V_{o}sin\theta_{2} t_{2}+\frac{gt_{2}^{2}}{2}$ (4)

Having this clear, let's begin with the answers:

a) Angle for snowball 2

Firstly, we have to isolate $t_{1}$ from (2):

$0=0+V_{o}sin\theta_{1} t_{1}+\frac{gt_{1}^{2}}{2}$ (5)

$t_{1}=-\frac{2V_{o}sin\theta_{1}}{g}$ (6)

Substituting (6) in (1):

$x=V_{o}cos\theta_{1}(-\frac{2V_{o}sin\theta_{1}}{g})$ (7)

Rewritting (7) and knowing $sin(2\theta)=sen\theta cos\theta$ :

$x=-\frac{V_{o}^{2}}{g} sin(2\theta_{1})$ (8)

$x=-\frac{(11.1 m/s)^{2}}{-9.8 m/s^{2}} sin(2(67\°))$ (9)

x=9.043 m (10) This is the point at which snowball 1 hits and snowball 2 should hit, too.

With this in mind, we have to isolate $t_{2}$ from (4) and substitute it on (3):

$t_{2}=-\frac{2V_{o}sin\theta_{2}}{g}$ (11)

$x=V_{o}cos\theta_{2} (-\frac{2V_{o}sin\theta_{2}}{g})$ (12)

Rewritting (12):

$x=-\frac{V_{o}^{2}}{g} sin(2\theta_{2})$ (13)

Finding $\theta_{2}$ :

$2\theta_{2}=sin^{-1}(\frac{-xg}{V_{o}^{2}})$ (14)

$2\theta_{2}=45.99\°$

$\theta_{2}=22.99\° \approx 23\°$ (15) This is the second angle at which snowball 2 must be thrown. Note this angle is lower than the first angle $(\theta_{2} < \theta_{1})$ .

b) Time difference between both snowballs

Now we will find the value of $t_{1}$ and $t_{2}$ from (6) and (11), respectively:

$t_{1}=-\frac{2V_{o}sin\theta_{1}}{g}$

$t_{1}=-\frac{2(11.1 m/s)sin(67\°)}{-9.8m/s^{2}}$ (16)

$t_{1}=2.085 s$ (17)

$t_{2}=-\frac{2V_{o}sin\theta_{2}}{g}$

$t_{2}=-\frac{2(11.1 m/s)sin(23\°)}{-9.8m/s^{2}}$ (18)

$t_{2}=0.885 s$ (19)

Since snowball 1 was thrown before snowball 2, we have:

$t_{1}-t=t_{2}$ (20)

Finding the time difference between both:

$t=t_{1}-t_{2}$ (21)

t=2.085 s - 0.885 s

Finally:

t=1.199 s

Answer from: Quest

hotter stars = bluer stars

Answer from: Quest

he made 11 calls in one day

Another question on Physics

Physics, 21.06.2019 16:20

When a resistor with resistance r is connected to a 1.50-v flashlight battery, the resistor consumes 0.0625 w of electrical power. (throughout, assume that each battery has negligible internal resistance.) what power does the resistor consume if it is connected to a 12.6-v car battery? assume that r remains constant when the power consumption changes.

Answers: 1

Answer

Physics, 22.06.2019 19:30

Scientist have use computer models to create a series of maps that show how susceptible coastal cities in island countries are to the sea rising at different levels.the map shows that a 1 meter rise would swap cities all along the us eastern seaboard. a 6-meter sea level rise with sub merge a large part of florida. thermal expansion has already raise the oceans 10 to 20 centimeters the most likely cause,directly and indirectly, for such a rise in sea level is

Answers: 2

Answer

Physics, 22.06.2019 23:00

Two horses begin at rest. after a few seconds, horse a is traveling with a velocity of 10 m/s west, while horse b is traveling with a velocity of 13 m/s west. which horse had a greater acceleration? a. horse a because its change in velocity was greater than horse b's in the same time. b. horse b because its change in velocity was greater than horse a's in the same time. c. horse b because its change in velocity was the same as horse a's, but it took less time. d. both horses had the same acceleration.

Answers: 1

Answer

Physics, 22.06.2019 23:30

Which statement correctly describes the interaction between magnetic poles? north and south poles attract each other. north and south poles repel each other. two north poles will attract each other. two south poles will attract each other.

Answers: 1

Answer

You know the right answer?

One strategy in a snowball fight is to throw
a snowball at a high angle over level ground.

Questions