1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dangina [55]
2 years ago
8

One strategy in a snowball fight is to throw

Physics
1 answer:
faltersainse [42]2 years ago
7 0

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: <u>x-component</u> and <u>y-component</u>. Being their main equations as follows for both snowballs:

<h3><u>Snowball 1:</u></h3>

<u>x-component: </u>

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

<u>y-component: </u>

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)

<h3><u>Snowball 2:</u></h3>

<u>x-component: </u>

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

<u>y-component: </u>

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:

<h2>a) Angle for snowball 2</h2>

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}).

<h2>b) Time difference between both snowballs</h2>

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 t between both:

t=t_{1}-t_{2}   (21)

t=2.085 s - 0.885 s  

Finally:

t=1.199 s  

You might be interested in
What does x repressent on a motion map?​
Gnoma [55]

Answer:

The x represents the reference point on a motion map

Explanation:

-Motion maps are another way to represent the motion of an object. (other representations are graphical and mathematical models)

6 0
3 years ago
Read 2 more answers
An athlete is running a 400m race around a 400m track. On the backstretch the athlete's velocity is 8m/s but he is running into
Aleksandr-060686 [28]

Answer:

33 N

Explanation:

v = Velocity of fluid = 8+2 = 10 m/s

\rho = Density of fluid = 1.2 kg/m³

C = Coefficient of drag = 1.1

A = Cross sectional area = 0.5 m²

Drag force is given by

F=\frac{1}{2}\rho CAv^2\\\Rightarrow F=\frac{1}{2}\times 1.2\times 1.1\times 0.5\times (8+2)^2\\\Rightarrow F=33\ N

The drag force on the athlete is 33 N

3 0
3 years ago
Determine the amount of work done on an ideal gas as it is heated in an enclosed thermally insulated cylinder topped with a free
sp2606 [1]

Answer:

W = 3/2 n (T₁- T₂)

Explanation:

Let's use the first law of thermodynamics

           ΔE = Q + W

in this case the cylinder is insulated, so there is no heat transfer

           ΔE = W

internal energy can be related to the change in temperature

            ΔE = 3/2 n K ΔT

we substitute

           3/2 n (T₂-T₁) = W

as the work is on the gas it is negative

            W = 3/2 n (T₁- T₂)

3 0
3 years ago
What is the relationship among amplitude,crest,and trough?
Musya8 [376]
These are characteristics of a wave. The amplitude is how high and low the waves go. Crests are high points on the wave, and troughs are low points on the wave.
5 0
3 years ago
Why do sound waves move faster through the ground than through the air? a. Particles of matter are packed more loosely in the gr
lbvjy [14]
B. is it i just got done this in class like two weeks ago hope it helps

5 0
3 years ago
Read 2 more answers
Other questions:
  • What form of energy provides power for a gas stove?
    8·2 answers
  • Is there is only one tool used to heat equipment in the laboratory.
    7·2 answers
  • A heat engine with a thermal efficiency of 45 percent rejects 500 kj/kg of heat. how much heat does it receive
    10·1 answer
  • When a compass needle settles down in a magnetic field, _______. the needle aligns itself with the field, the south end of the c
    8·1 answer
  • An old clock has a spring that must be wound to make the clock hands move. Which statement describes the energy of the spring an
    13·2 answers
  • The results of a dart game were precise but not accurate. The accepted value of the game was the center of the dartboard. Which
    13·2 answers
  • PLEASE HELP PHYSICS!!!!! WILL MARK BRAINLIEST IF CORRECT!!!!
    11·2 answers
  • A parallel combination of a 1.13-μF capacitor and a 2.85-μF one is connected in series to a 4.25-μF capacitor. This three-capaci
    11·1 answer
  • how can you find the mechanical advantage of the six different simple machines? (simples mechinals are pulleys, inclined plane,
    9·1 answer
  • Explain how ozone is both beneficial and detrimental to human health.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!