Question

you are playing tag with your friend on cool math games. pink unicorn is running away from green alien. you are trying to reach the top platform to escape. you jump 187.0 pixels at 58.0 degrees from the ground to get to the first platform. then, you run 100.0 pixels to the left parallel to the ground. you jump 224.0 pixels at 48.0 degrees from the ground to get to the highest platform and finally run 63.0 pixels to the right parallel to the ground. find your displacement.

Explanation:

Step1: Resolve the first - jump components

The first jump has magnitude $d_1 = 187.0$ pixels and angle $\theta_1=58.0^{\circ}$. The horizontal component $x_1=d_1\cos\theta_1$ and the vertical component $y_1 = d_1\sin\theta_1$.
$x_1=187.0\cos(58.0^{\circ})\approx187.0\times0.5299 = 99.1913$ pixels
$y_1=187.0\sin(58.0^{\circ})\approx187.0\times0.8480 = 158.576$ pixels

Step2: Account for the first horizontal run

The first horizontal run is $x_2=- 100.0$ pixels (negative because it's to the left).

Step3: Resolve the second - jump components

The second jump has magnitude $d_2 = 224.0$ pixels and angle $\theta_2 = 48.0^{\circ}$. The horizontal component $x_3=d_2\cos\theta_2$ and the vertical component $y_2=d_2\sin\theta_2$.
$x_3=224.0\cos(48.0^{\circ})\approx224.0\times0.6691=149.8784$ pixels
$y_2=224.0\sin(48.0^{\circ})\approx224.0\times0.7431 = 166.4544$ pixels

Step4: Account for the second horizontal run

The second horizontal run is $x_4 = 63.0$ pixels (positive because it's to the right).

Step5: Calculate the total horizontal displacement

$x=x_1 + x_2+x_3+x_4=99.1913-100.0 + 149.8784+63.0=212.0697$ pixels

Step6: Calculate the total vertical displacement

$y=y_1 + y_2=158.576+166.4544 = 325.0304$ pixels

Step7: Calculate the magnitude of the displacement

The magnitude of the displacement $D$ is given by $D=\sqrt{x^{2}+y^{2}}$.
$D=\sqrt{(212.0697)^{2}+(325.0304)^{2}}$
$D=\sqrt{44974.77+105645.97}$
$D=\sqrt{150620.74}\approx388$ pixels

Answer:

Approximately 388 pixels