<span>et us assume that the origin is the floor right below the 30 ft. fence
To work this one out, we'll start with acceleration and integrate our way up to position.
At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.
To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
vy = -gt + v0y = -32.8t + v0sin40 = -32.8t + 60
To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4
If the ball clears the fence, it means x = 0, y > 30
x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds
for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
= 20.45 ft
which is less than 30ft, so it means that the ball will NOT clear the fence.
Just for fun, let's check what the speed should have been :)
x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4
x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s
v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s
So he needed to hit the ball at at least 123.34 ft/s to clear the fence.
You're welcome, Thanks please :)
</span>
Answer:
4√10xy/32y is the answer. (I think)
Answer:
B) Isolate the variable through inverse operations
Step-by-step explanation:
In order to get the value of y, we need to get y by itself. Since y is being multiplied by the coefficient 7, dividing both sides by 7 gets us y=10, so B is the right choice.
Answer:
Step-by-step explanation:
<h3><u>Given that:</u></h3>
Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
<h3><u>Statement:</u></h3>
- Exterior angle is equal to the sum of non-adjacent interior angles.
So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
<h3><u>Measure of angle M:</u></h3>
= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
<h3><u>Measure of angle L:</u></h3>
<u>We know that,</u>
- Sum of all the interior angles of triangle is 180 degrees.
L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
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Answer:
2/7.
Step--step explanation:
1/2 * 4/7.
Multiply the numerators and the denominators:
= 1*4 / 2*7
= 4 / 14 Now divide numerator and denominator by 2:
= 2/7.
