B. It is the only graph that accurately describes acceleration as speed gradually increases.
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Complete question is;
a. Two equal sized and shaped spheres are dropped from a tall building. Sphere 1 is hollow and has a mass of 1.0 kg. Sphere 2 is filled with lead and has a mass of 9.0 kg. If the terminal speed of Sphere 1 is 6.0 m/s, the terminal speed of Sphere 2 will be?
b. The cross sectional area of Sphere 2 is increased to 3 times the cross sectional area of Sphere 1. The masses remain 1.0 kg and 9.0 kg, The terminal speed (in m/s) of Sphere 2 will now be
Answer:
A) V_t = 18 m/s
B) V_t = 10.39 m/s
Explanation:
Formula for terminal speed is given by;
V_t = √(2mg/(DρA))
Where;
m is mass
g is acceleration due to gravity
D is drag coefficient
ρ is density
A is Area of object
A) Now, for sphere 1,we have;
m = 1 kg
V_t = 6 m/s
g = 9.81 m/s²
Now, making D the subject, we have;
D = 2mg/((V_t)²ρA))
D = (2 × 1 × 9.81)/(6² × ρA)
D = 0.545/(ρA)
For sphere 2, we have mass = 9 kg
Thus;
V_t = √[2 × 9 × 9.81/(0.545/(ρA) × ρA))]
V_t = 18 m/s
B) We are told that The cross sectional area of Sphere 2 is increased to 3 times the cross sectional area of Sphere 1.
Thus;
Area of sphere 2 = 3A
Thus;
V_t = √[2 × 9 × 9.81/(0.545/(ρA) × ρ × 3A))]
V_t = 10.39 m/s
Answer:
The correct option is C
Explanation:
According to third equation of motion, v
2
=u
2
+2ax
Here, u=0 m/s
a=−g and x=−h
Negative sign indicates downward direction. Displacement and acceleration both are downwards.
So,v=±
2(−g)(−h)
We take minus sign because it is downwards.
v=−
2gh
After bouncing. velocity becomes 80% of v, i.e.,
v
′
=+0.8
2gh
(positive sign because the direction of ball has reversed after bouncing and is upwards.
Applying third equation of motion again, for u=v
′
, v=0 and a=−g
v
2
=u
2
+2×a×x
Thus,
0=0.64(2gh)+2(−g)x
or
x=0.64h