Explanation:
Those tools that helps to make our work easier ,faster and more convenient in our daily life it is called simple Machine.
Answer:
66.85 m
Explanation:
We are given that
Acceleration ,a=![2.7m/s^2](https://tex.z-dn.net/?f=2.7m%2Fs%5E2)
Speed of truck, v=9.5 m/s
We have to find the distance beyond which the traffic signal will the automobile overtake the truck.
Initial speed of automobile, u=0
We know that
![s=ut+\frac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
Using the formula
![s=0+\frac{1}{2}(27)t^2=\frac{27}{2}t^2](https://tex.z-dn.net/?f=s%3D0%2B%5Cfrac%7B1%7D%7B2%7D%2827%29t%5E2%3D%5Cfrac%7B27%7D%7B2%7Dt%5E2)
For constant speed
Acceleration, a=0
Again
![s=vt+0=9.5t](https://tex.z-dn.net/?f=s%3Dvt%2B0%3D9.5t)
![9.5t=\frac{27}{2}t^2](https://tex.z-dn.net/?f=9.5t%3D%5Cfrac%7B27%7D%7B2%7Dt%5E2)
![t=\frac{9.5\times 2}{2.7}=7.037s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B9.5%5Ctimes%202%7D%7B2.7%7D%3D7.037s)
Substitute the value of t
![x=9.5(7.037)=66.85m](https://tex.z-dn.net/?f=x%3D9.5%287.037%29%3D66.85m)
Hence, the distance beyond which the traffic signal will the automobile overtake the truck=66.85 m
Answer:
We are given the trajectory of a projectile:
y=H+xtan(θ)−g2u2x2(1+tan2(θ)),
where H is the initial height, g is the (positive) gravitational constant and u is the initial speed. Since we are looking for the maximum range we set y=0 (i.e. the projectile is on the ground). If we let L=u2/g, then
H+xtan(θ)−12Lx2(1+tan2(θ))=0
Differentiate both sides with respect to θ.
dxdθtan(θ)+xsec2(θ)−[1Lxdxdθ(1+tan2(θ))+12Lx2(2tan(θ)sec2(θ))]=0
Solving for dxdθ yields
dxdθ=xsec2(θ)[xLtan(θ)−1]tan(θ)−xL(1+tan2(θ))
This derivative is 0 when tan(θ)=Lx and hence this corresponds to a critical number θ for the range of the projectile. We should now show that the x value it corresponds to is a maximum, but I'll just assume that's the case. It pretty obvious in the setting of the problem. Finally, we replace tan(θ) with Lx in the second equation from the top and solve for x.
H+L−12Lx2−L2=0.
This leads immediately to x=L2+2LH−−−−−−−−√. The angle θ can now be found easily.
Explanation:
Wind resistance is a kind of friction we usually try to minimize. It makes our cars and planes run less efficiently. At the same time though, we need friction between our tires and the road to move, as well as friction in our brakes to stop. We wouldn't be able to walk without friction, or start a campfire by rubbing sticks together.