Answer:
5.25 m
Explanation:
Given;
The height equation h;
h=-x^2+3x+3
Where;
h = the height above water
x = horizontal distance from the end of the board
The maximum height is at h' = 0, when change in h with respect to change in x is equal to zero.
differentiating the equation h.
dh/dx = h' = -2x + 3 = 0
Solving for x;
2x = 3
x = 3/2
Substituting into the function h;
h max = -x^2+3x+3
h max = -(3/2)^2 + 3(3/2) +3 = -9/4 +9/2 +3 = 9/4 + 3 =
h max = 21/4 = 5.25 m
<span>Step 1 -- determine the acceleration of the 200-g block after bullet hits it
a = (coeff of friction) * g
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
a = 0.400*9.8
a = 3.92 m/sec^2
Step 2 -- determine the speed of the block after the bullet hits it
Vf^2 - Vb^2 = 2(a)(s)
where
Vf = final velocity = 0 (since it will stop)
Vb = velocity of block after bullet hits it
a = -3.92 m/sec^2
s = stopping distance = 8 m (given)
Substituting values,
0 - Vb^2 = 2(-3.92)(8)
Vb^2 = 62.72
Vb = 7.92 m/sec.
M1V1 + M2V2 = (M1 + M2)Vb
where
M1 = mass of the bullet = 10 g (given) = 0.010 kg.
V1 = velocity of bullet before impact
M2 = mass of block = 200 g (given) = 0.2 kg.
V2 = initial velocity of block = 0
Vb = 7.92 m/sec
Substituting values,
0.010(V1) + 0.2(0) = (0.010 + 0.2)(7.92)
Solving for V1,
V1 = 166.32 m/sec.
Therefore the answer is (B) 166 m/s!</span>
Answer:
Density of a substance is the ratio of mass of the substance to its volume.
Determinatio/Goal setting
