Physics, 14.09.2019 07:30 robert7248

Acar is driven east for a distance of 48 km, then north for 29 km, and then in a direction 30° east of north for 29 km. determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

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Answer from: madivassallo

a) The magnitude of the car's total displacement (T) from the starting point is T = 82.67 Km

b) The angle (θ) from east of the car's total displacement measured from the starting direction is θ = 40.88 °

Explanation:

Attached you can see a diagram of the problem.

a) Find the magnitude of the vector T that goes from point A to point D (see the diagram).

The x and y components of this vector are

$T_x=48+29*sin(30)=62.5 Km\\T_y=29+29*cos(30) = 54.11 Km$

The magnitude of the vector is find using the pythagoras theorem:

a^2=b^2+c^2 , being a, b and c the 3 sides of the triagle that forms the vector:

$T^2=T_x^2+T_y^2\\T=\sqrt{T_x^2+T_y^2}$

Replacing the values

$T=\sqrt{(62.5)^2+(54.11)^2} \\T=82.67 Km$

b) Find the angle θ that forms the vector T and the vector AB (see diagram).

To find this angle you can use the inverse tangent

θ $=tan^{-1}(\frac{T_y}{T_x})$

θ $=tan^{-1}(\frac{54.11}{62.5})$

θ=40.88°

Acar is driven east for a distance of 48 km, then north for 29 km, and then in a direction 30° east

Answer from: Quest

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

$a = 32 ft/s^2$

so as we know that

$a = \frac{v^2}{r}$

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

$a_c = 32 ft/s^2$

$a_t = 0$

now radius of curvature is given as

$r = \frac{v^2}{a_c}$

$r = \frac{150^2}{32}$

$r = 703.125ft$

so the radius of curvature just after it is dropped is 703.125 ft

Answer from: Quest

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.

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Acar is driven east for a distance of 48 km, then north for 29 km, and then in a direction 30° east...