Answer:
b. v = 0, a = 9.8 m/s² down.
Explanation:
Hi there!
The acceleration of gravity is always directed to the ground (down) and, near the surface of the earth, has a constant value of 9.8 m/s². Since the answer "b" is the only option with an acceleration of 9.8 m/s² directed downwards, that would solve the exercise. But why is the velocity zero at the highest point?
Let´s take a look at the height function:
h(t) = h0 + v0 · t + 1/2 g · t²
Where
h0 = initial height
v0 = initial velocity
t = time
g = acceleration due to gravity
Notice that the function is a negative parabola if we consider downward as negative (in that case "g" would be negative). Then, the function has a maximum (the highest point) at the vertex of the parabola. At the maximum point, the slope of the tangent line to the function is zero, because the tangent line is horizontal at a maximum point. The slope of the tangent line to the function is the rate of change of height with respect to time, i.e, the velocity. Then, the velocity is zero at the maximum height.
Another way to see it (without calculus):
When the ball is going up, the velocity vector points up and the velocity is positive. After reaching the maximum height, the velocity vector points down and is negative (the ball starts to fall). At the maximum height, the velocity vector changed its direction from positive to negative, then at that point, the velocity vector has to be zero.
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Answer:
Total momentum = 50kgm/s
Explanation:
<u>Given the following data;</u>
Mass, M1 = 5kg
Mass, M2 = 7kg
Velocity, V1 = 10m/s
Velocity, V2 = 0m/s (since it's at rest).
To find the total momentum;
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
The law of conservation of momentum states that the total linear momentum of any closed system would always remain constant with respect to time.
Total momentum = M1V1 + M2V2
Substituting into the equation, we have;
Total momentum = 5*10 + 7*0
Total momentum = 50 + 0
<em>Total momentum = 50 kgm/s</em>
<em>Therefore, the total momentum of the bowling ball and the putty after they collide is 50 kgm/s. </em>
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