Answer:
a =( -0.32 i ^ - 2,697 j ^) m/s²
Explanation:
This problem is an exercise of movement in two dimensions, the best way to solve it is to decompose the terms and work each axis independently.
Break down the speeds in two moments
initial
v₀ₓ = v₀ cos θ
v₀ₓ = 5.25 cos 35.5
v₀ₓ = 4.27 m / s
= v₀ sin θ
= 5.25 sin35.5
= 3.05 m / s
Final
vₓ = 6.03 cos (-56.7)
vₓ = 3.31 m / s
= v₀ sin θ
= 6.03 sin (-56.7)
= -5.04 m / s
Having the speeds and the time, we can use the definition of average acceleration that is the change of speed in the time order
a = (
- v₀) /t
aₓ = (3.31 -4.27)/3
aₓ = -0.32 m/s²
= (-5.04-3.05)/3
= -2.697 m/s²
Answer:
12.6 cm
Explanation:
We can use the mirror equation to find the distance of the image from the mirror:

where here we have
f = 9.50 cm is the focal length
p = 39 cm is the distance of the object from the mirror
Solving the equation for q, we find:

The alpha line in the Balmer series is the transition from n=3 to n=2 and with the wavelength of λ=656 nm = 6.56*10^-7 m. To get the frequency we need the formula: v=λ*f where v is the speed of light, λ is the wavelength and f is the frequency, or c=λ*f. c=3*10^8 m/s. To get the frequency: f=c/λ. Now we input the numbers: f=(3*10^8)/(6.56*10^-7)=4.57*10^14 Hz. So the frequency of the light from alpha line is f= 4.57*10^14 Hz.
Answer:
-24.28571 rad/s²
29.57239 revolutions
3.91176 seconds
52.026478 m
Explanation:
= Tangential acceleration = -6.8 m/s²
r = Radius of wheel = 0.28
= Initial angular velocity = 95 rad/s
= Angle of rotation
= Final angular velocity
t = Time taken
Angular acceleration is given by

The angular acceleration is -24.28571 rad/s²

The number of revolutions is 29.57239

The time it takes for the car to stop is 3.91176 seconds
Linear distance

The distance the car travels is 52.026478 m
Answer:
The distance is 0.53 m.
Explanation:
Given that,
Target distance = 100.0 m
Speed of bullet = 300 m/s
We need to calculate the total time
Using formula of time

Put the value into the formula


Now, consider vertical motion of bullet.
Initial velocity of bullet in vertical direction = 0 m/s
We need to calculate the vertically distance
Using equation of motion

Put the value in the equation


Hence, The distance is 0.53 m.