Answer:
8.9 seconds
Explanation:
The height of the object at time t is:
y = h + vt − 4.9t²
where h is the initial height, and v is the initial velocity.
Given h = 30 and v = 40:
y = 30 + 40t − 4.9t²
When y = 0:
0 = 30 + 40t − 4.9t²
4.9t² − 40t − 30 = 0
Solving with quadratic formula:
t = [ -(-40) ± √((-40)² − 4(4.9)(-30)) ] / 2(4.9)
t = [ 40 ± √(1600 + 588) ] / 9.8
t = 8.9
It takes 8.9 seconds for the object to land.
1. What is the force of the marble?
For an object near the surface of the earth, the gravitational force acting upon the object is given by:
F = mg
F is the gravitational force, m is the object's mass, and g is the acceleration of objects due to earth's gravity.
Given values:
m = 0.025kg, g = 9.8m/s²
Plug in the given values and solve for F:
F = 0.025×9.8
F = 0.25N
2. What is the marble's potential energy at the start of its fall?
The gravitational potential energy of an object near the earth's surface is given by:
PE = mgh
PE is the potential energy, m is the object's mass, g is the acceleration of objects due to earth's gravity, and h is the object's relative height.
new given values:
h = 0.08m
Since F = mg, you can simply multiply F×h to get PE. Use the result from question 1:
PE = F×h
PE = 0.25×0.08
PE = 0.02J
J=joules, c=specific heat, q= energy, and the Tf and Ti are the final and initial temperatures cause I couldn't find a delta sign.
To calculate the mass of the fuel, we use the formula
Here, m is the mass of fuel, V is the volume of the fuel and its value is and is the density and its value of 0.821 g/mL.
Substituting these values in above relation, we get
Thus, the mass of the fuel 247 .94 kg.