A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35.00 degrees above the horizontal. The ba
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Answer:
b) d = 997.9 m , c) D = (952.9 i ^ +45 k ^) m , D = 953.6 m and θ = 2.7º
Explanation:
In this exercise we must add the distance traveled, remembering that the displacement is a vector and the distance a scalar.
a) The displacement scheme is the woman walks in her building A to descend to the lower floor 4.0 m, we assume that this includes the vertical displacement, until reaching the street level, the displacement is vertical in this part.
Being on the street, she travels the 6.5 blocks to reach the building where she works, they indicate that each block is 146.6 m, this movement is horizontal.
Upon reaching building B, she goes up to his office on the 14th floor where she travels 5.5m on each floor, it is assumed that the distance to go up to the upper floor is included, this displacement is vertical
b and c) Let's find the distance traveled and the displacement
in building A
Zₐ = 8 * 4.0
Zₐ = -32.0 m k ^
the vector k ^ indicates that the displacement is vertical and the negative sign that it is descending
on the street
= 6.5 146.6
X_{ab} = 952.9 m i ^
the vector i ^ indicates that the displacement is the x-axis, we assume that the axis is in the direction of the displacement
in building B
= 14 * 5.5
Z_{b} = 77 m k ^
displacement in the vertical axis and in the positive direction
now we calculate the distance traveled,
d = Zₐ + X_{ab} + Z_{b}
d = -32 + 952.9 + 77
d = 997.9 m
note that this value is a scalar
Let's calculate the displacement,
Z axis
= Zₐ + Z_{b}
Z_{total} = -32 + 77
Z_{total} = 45 m k ^
X axis
X_{total} = X_{ab}
X_{total} = 952.9 m i ^
we can give the result in two ways
a) D = X_total i ^ + Z_total k ^
D = (952.9 i ^ +45 k ^) m
b) in module form and angles
Let's use the Pythagorean theorem
D² = +
D = √(952.9² + 45²)
D = 953.6 m
We use trigonometry
tan θ = Z / X
θ = tan⁻¹ (Z / X)
θ = tan⁻¹ (45 / 952.9)
θ = 2.7º
this angle is measured from the positive side of the x axis towards the z axis
ANSWER
75.65 km/h
EXPLANATION
Given:
• The student's mass, m = 77 kg
,• The kinetic energy of the student in the car, KE = 1.7 x 10⁴ J
Find:
• The speed read in the speedometer of the car, which is the speed of the student, v (in km/h)
The kinetic energy of an object with mass m, traveling at a speed v, is,
Solving for v,
Replace the known values and solve,
Note that because the kinetic energy is given in Joules - which is equivalent to kg*m²/s², the speed we found is in m/s. Now, knowing that there are 3600 seconds in 1 hour and that 1 km is equivalent to 1000 m, we can convert this to km/s,
Hence, the speedometer reading of the car is 75.65 km/h, rounded to the nearest hundredth.