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
Alex Ar [27]
3 years ago
11

A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0o above the horizontal towar

d the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part (a), how far does the shell land past the edge of the cliff?
Physics
1 answer:
Artist 52 [7]3 years ago
8 0

Answer:

a)   v₀ = 32.64 m / s , b)  x = 59.68 m

Explanation:

a) This is a projectile launching exercise, we the distance and height of the cliff

         x = v₀ₓ t

         y = v_{oy} t - ½ g t²

We look for the components of speed with trigonometry

         sin 43 = v_{oy} / v₀

         cos 43 = v₀ₓ / v₀

         v_{oy} = v₀ sin 43

         v₀ₓ = v₀ cos 43

Let's look for time in the first equation and substitute in the second

         t = x / v₀ cos 43

         y = v₀ sin 43 (x / v₀ cos 43) - ½ g (x / v₀ cos 43)²

          y = x tan 43 - ½ g x² / v₀² cos² 43

          1 / v₀² = (x tan 43 - y) 2 cos² 43 / g x²

           v₀² = g x² / [(x tan 43 –y) 2 cos² 43]

Let's calculate

          v₀² = 9.8 60 2 / [(60 tan 43 - 25) 2 cos 43]

          v₀ = √ (35280 / 33.11)

          v₀ = 32.64 m / s

.b) we use the vertical distance equation with the speed found

         y = v_{oy} t - ½ g t²

         .y = v₀ sin43 t - ½ g t²

        25 = 32.64 sin 43 t - ½ 9.8 t²

        4.9 t² - 22.26 t + 25 = 0

         t² - 4.54 t + 5.10 = 0

We solve the second degree equation

         t = (4.54 ±√(4.54 2 - 4 5.1)) / 2

         t = (4.54 ± 0.46) / 2

         t₁ = 2.50 s

         t₂ = 2.04 s

The shortest time is when the cliff passes and the longest when it reaches the floor, with this time we look for the horizontal distance traveled

         x = v₀ₓ t

         x = v₀ cos 43 t

         x = 32.64 cos 43  2.50

         x = 59.68 m

You might be interested in
Two satellites are in circular orbits around the earth. the orbit for satellite a is at a height of 542 km above the earth's sur
Evgen [1.6K]
Let R be radius of Earth with the amount of 6378 km h = height of satellite above Earth m = mass of satellite v = tangential velocity of satellite 
Since gravitational force varies contrariwise with the square of the distance of separation, the value of g at altitude h will be 9.8*{[R/(R+h)]^2} = g' 
So now gravity acceleration is g' and gravity is balanced by centripetal force mv^2/(R+h): 
m*v^2/(R+h) = m*g' v = sqrt[g'*(R + h)] 
Satellite A: h = 542 km so R+h = 6738 km = 6.920 e6 m g' = 9.8*(6378/6920)^2 = 8.32 m/sec^2 so v = sqrt(8.32*6.920e6) = 7587.79 m/s = 7.59 km/sec 
Satellite B: h = 838 km so R+h = 7216 km = 7.216 e6 m g' = 9.8*(6378/7216)^2 = 8.66 m/sec^2 so v = sqrt(8.32*7.216e6) = 7748.36 m/s = 7.79 km/sec
6 0
3 years ago
When you trace the outline of your palm how do you find its area​
Tcecarenko [31]

Answer:

you count the squares or messure it

Explanation:

you can raw equal squares about 1 cm wide if possible all equal and count the squares eg theres 10 squares (small hand) so that would be 10cm squared

7 0
3 years ago
Read 2 more answers
A skateboarder drops in off the top of one side of the half pipe shown below. She does not push off and starts from rest. She st
solong [7]

Answer:

v

Explanation:

4 0
2 years ago
The jet stream flows from east to west across the United States.<br><br><br> True False
velikii [3]
This is false. they flow west to east
8 0
3 years ago
Read 2 more answers
Why must objects be cooled before their mass is determined on a sensitive balance?
zubka84 [21]
Objects should be cooled before their mass is determined on a sensitive balance because it could damage the balance. Also, because it would give you wrong reading of the mass. Hot objects would warm the air around it. A warm air would expand and would produce convection as it rises causing to give the object a mass that is less than the actual. Another reason would be it would cause instability in the readings, the mass would fluctuate every now and then due to the convection currents around the object. It is always recommended to weigh the masses of objects that are in room temperature.
5 0
3 years ago
Other questions:
  • During combustion, a fuel’s electromagnetic energy is converted into thermal energy.
    15·1 answer
  • Which of the following is a negatively charged particle that is found in "clouds" around the nucleus?
    9·1 answer
  • The intensity of light from a central source varies inversely as the square of the distance. If you lived on a planet only half
    15·1 answer
  • What effect does freezing water into a ice cube have on its mass
    12·1 answer
  • Which chart provides the correct number of neutrons for each isotope of tin (Sn)?
    14·1 answer
  • What are the connective cells
    7·1 answer
  • A circular wooden loop of mass m and radius R rest on a flat horizontal friction less surface. A bullet, also of mass m, and mov
    14·1 answer
  • What's the average speed of an object moving 3790 meters in 249 s.
    12·1 answer
  • Porque al tomar agua y la dejo en mi boca no se baja? Curiosidad xd
    14·1 answer
  • Please help ASAP....
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!