HELP WITH THESE PLEASE!
If you ride your bike at an average speed of 4km/h and nee to travel a total distance of 28 km, how long will it take you to reach your destination?
A small dog is trained to jump straight up a distance of 1.2 m. How much kinetic energy does the 7.2-kg dog need to jump this high? ( the acceleration due to gravity is 9.8 m/s^2
As 390 g of hot milk cools in a mug, it transfers 30,000 J of heat to the environment. What is the temperature change of the milk? The specific heat of the milk is 3.9 J/g*C.
I Need to Be able to show all my work
1)
t=s/v= 28/4 = 7 hr
2)
KE=PE=mgh =7.2 •9.8•1.2 = …J
3)
Q=mcΔT
ΔT= Q/mc = 30000/0.39•3.9 = …
Sure! Let's go through each problem step by step.
Problem 1:
To find the time it will take to reach the destination, we can use the formula: time = distance / speed.
Given:
- Average speed = 4 km/h
- Total distance = 28 km
So, we can substitute these values into the formula to get: time = 28 km / 4 km/h
To simplify the calculation, let's convert everything to the same unit. We know that 1 km is equal to 1000 meters (m), and 1 hour is equal to 3600 seconds (s).
Therefore, speed = 4 km/h = 4 * 1000 m / 3600 s = 4000 m / 3600 s = 10/9 m/s
distance = 28 km = 28 * 1000 m = 28000 m
Now we can plug these values into the formula: time = 28000 m / (10/9 m/s)
To divide by a fraction, we can multiply by the reciprocal of that fraction:
time = 28000 m * (9/10 m/s) = 252000/10 = 25200/100 = 252 seconds
Therefore, it will take you 252 seconds (or 4 minutes and 12 seconds) to reach your destination.
Problem 2:
To calculate the kinetic energy, we can use the formula: kinetic energy = 1/2 * mass * velocity^2.
Given:
- Mass of the dog (m) = 7.2 kg
- Distance (height) jumped (h) = 1.2 m
- Acceleration due to gravity (g) = 9.8 m/s^2
First, let's calculate the velocity (v) of the dog when it jumps to the given height using the equation: v^2 = 2gh, where g is the acceleration due to gravity.
v^2 = 2 * 9.8 m/s^2 * 1.2 m = 23.52 m^2/s^2
v = sqrt(23.52 m^2/s^2) ≈ 4.85 m/s
Now we can substitute the values into the kinetic energy formula: kinetic energy = 1/2 * mass * (velocity)^2
kinetic energy = 1/2 * 7.2 kg * (4.85 m/s)^2
Calculating this would give you the value of the kinetic energy in joules.
Problem 3:
To find the temperature change of the milk, we can use the formula: heat transferred = mass * specific heat * temperature change.
Given:
- Mass of the milk (m) = 390 g
- Specific heat of the milk (c) = 3.9 J/g°C
- Heat transferred (q) = 30,000 J
Rearranging the formula, we can solve for the temperature change:
temperature change = heat transferred / (mass * specific heat)
temperature change = 30,000 J / (390 g * 3.9 J/g°C)
Simplifying this would give you the temperature change in degrees Celsius.
Remember, when solving problems like these, it's important to properly convert units and use the correct formulas.