Answer:
a) t = 4.16 s
b) x = 141.51 m
Explanation:
Given
v = 21.5 m/s
x0 = 52.0 m
a = 6.0 m/s²
a) Motorcycle
x = v0*t + (a*t²/2)
x = 21.5t + (6*t²/2)
x = 21.5t + 3t² <em>(I)</em>
Car
x = x0 + v0*t
x = 52 + 21.5t <em>(II)</em>
<em />
then we can apply <em>I = II</em>
21.5t + 3t² = 52 + 21.5t
⇒ 3t² = 52
⇒ t = 4.16 s
b) We can use <em>I</em> or <em>II</em>, then
x = 52 + 21.5*(4.16)
⇒ x = 141.51 m
Answer:
+7.0 m/s
Explanation:
Let's take rightward as positive direction.
So in this problem we have:
a = -2.5 m/s^2 acceleration due to the wind (negative because it is leftward)
t = 4 s time interval
v = -3.0 m/s is the final velocity (negative because it is leftward)
We can use the following equation:
v = u + at
Where u is the initial velocity
We want to find u, so if we rearrange the equation we find:
![u = v - at = (-3.0 m/s) - (-2.5 m/s^2)(4 s)=+7.0 m/s](https://tex.z-dn.net/?f=u%20%3D%20v%20-%20at%20%3D%20%28-3.0%20m%2Fs%29%20-%20%28-2.5%20m%2Fs%5E2%29%284%20s%29%3D%2B7.0%20m%2Fs)
and the positive sign means the initial direction was rightward.
Answer:
D
Explanation:
<em>The most suitable testable question. in this case, would be that 'are there more home runs during the more humid months of the summer?'</em>
Since the aim of the investigation is to find the relationship between humidity and the number of home runs, measuring the number of home runs during the more humid months in the summer and comparing the data to the number of home runs during the less humid months in the same summer would provide the answer.
<u>Only option D raises a valid question that is relevant to the aim of the investigation.</u>
Answer:
The center of mass of three mass in the x-y plane is located at (1,0.5).
Explanation:
It is given that, a mass of 6 kg is at (0,0), a mass of 4 kg is at (3,0), and a mass of 2 kg is at (0,3). We need to find the center of mass of the system. Center of mass in x direction is :
![C_x=\dfrac{6\times 0+4\times 3+2\times 0}{6+4+2}\\\\C_x=1](https://tex.z-dn.net/?f=C_x%3D%5Cdfrac%7B6%5Ctimes%200%2B4%5Ctimes%203%2B2%5Ctimes%200%7D%7B6%2B4%2B2%7D%5C%5C%5C%5CC_x%3D1)
The center of mass in y direction is :
![C_y=\dfrac{6\times 0+4\times 0+2\times 3}{6+4+2}\\\\C_y=0.5](https://tex.z-dn.net/?f=C_y%3D%5Cdfrac%7B6%5Ctimes%200%2B4%5Ctimes%200%2B2%5Ctimes%203%7D%7B6%2B4%2B2%7D%5C%5C%5C%5CC_y%3D0.5)
So, the center of mass of three mass in the x-y plane is located at (1,0.5).
Explanation:
Let us first calculate long does it take to go 12m at 30m/s( assumed speed)
12/30 = 0.4 seconds
horizontal distance the ball drop in that time
H= (0)(0.4)+1/2(-9.8)(0.4)2
H= -0.78m
negative sign shows that the height of the ball at the net from the top.
Height of the ball at the net and from the ground= H1-H=2.4-0.78=1.62m
As 1.62m>0.9m so the ball will clear the net.
H_1= V0y t’ + ½ g t’^2
-2.4= (0)t’ + ½ (-9.8) t’^2
t’= 0.69s
X’=V0x t’
X’=(30)(0.96)
X’= 20.7m