Presentation is loading. Please wait.

Presentation is loading. Please wait.

EXAMPLE 5 Calculate horizontal distance traveled Robotics

Similar presentations


Presentation on theme: "EXAMPLE 5 Calculate horizontal distance traveled Robotics"— Presentation transcript:

1 EXAMPLE 5 Calculate horizontal distance traveled Robotics The “frogbot” is a robot designed for exploring rough terrain on other planets. It can jump at a 45° angle and with an initial speed of 16 feet per second. On Earth, the horizontal distance d (in feet) traveled by a projectile launched at an angle θ and with an initial speed v (in feet per second) is given by: d = v2 32 sin 2θ How far can the frogbot jump on Earth?

2 Calculate horizontal distance traveled
EXAMPLE 5 Calculate horizontal distance traveled SOLUTION d = v2 32 sin 2θ Write model for horizontal distance. d = 162 32 sin (2 45°) Substitute 16 for v and 45° for θ. = 8 Simplify. The frogbot can jump a horizontal distance of 8 feet on Earth.

3 EXAMPLE 6 Model with a trigonometric function A rock climber is using a rock climbing treadmill that is 10.5 feet long. The climber begins by lying horizontally on the treadmill, which is then rotated about its midpoint by 110° so that the rock climber is climbing towards the top. If the midpoint of the treadmill is 6 feet above the ground, how high above the ground is the top of the treadmill? Rock climbing

4 Model with a trigonometric function
EXAMPLE 6 Model with a trigonometric function SOLUTION sin θ = y r Use definition of sine. sin 110° = y 5.25 Substitute 110° for θ and = 5.25 for r. 2 10.5 y Solve for y. The top of the treadmill is about = 10.9 feet above the ground.

5 The long jumper can jump 14.64 feet.
GUIDED PRACTICE for Examples 5 and 6 TRACK AND FIELD 10. Estimate the horizontal distance traveled by a track and field long jumper who jumps at an angle of 20° and with an initial speed of 27 feet per second. SOLUTION d = v2 32 sin 2θ Write model for horizontal distance. d = 272 32 sin (2 20°) Substitute 27 for v and 20° for θ. = Simplify. The long jumper can jump feet.

6 GUIDED PRACTICE for Examples 5 and 6 11.
WHAT IF? In Example 6, how high is the top of the rock climbing treadmill if it is rotated 100° about its midpoint? SOLUTION sin θ = y r Use definition of sine. sin 100° = y 5.25 Substitute 100° for θ and = 5.25 for r. 2 10.5 y Solve for y. The top of the treadmill is about = 11.2 feet above the ground.


Download ppt "EXAMPLE 5 Calculate horizontal distance traveled Robotics"

Similar presentations


Ads by Google