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A circus acrobat is launched by a catapult at a speed of 15.0 [m] at an angle of 0 = 40.0° above the horizontal as shown. At a distance of 20.0 [m] away, her partner is standing on a platform at a height of h meters. At the instant that the acrobat is launched, her partner throws a basketball towards her horizontally at a speed of 5.00 [m/s]. Ignore air resistance in solving this problem. -20 m y A 5 m/s 15 m/s origin (a) Write equations for the horizontal and vertical positions as functions of time for both the acrobat and the basketball. Use the coordinate system prescribed in the diagram. (b) When will the acrobat and basketball be at the same horizontal position? (c) Find the value of h for which the acrobat will catch the ball. Assume that she and the ball must be at the same height for her to catch it.

A circus acrobat is launched by a catapult at a speed of 15.0 [m] at an angle of 0 = 40.0° above the horizontal as shown. At a distance of 20.0 [m] away, her partner is standing on a platform at a height of h meters. At the instant that the acrobat is launched, her partner throws a basketball towards her horizontally at a speed of 5.00 [m/s]. Ignore air resistance in solving this problem. -20 m y A 5 m/s 15 m/s origin (a) Write equations for the horizontal and vertical positions as functions of time for both the acrobat and the basketball. Use the coordinate system prescribed in the diagram. (b) When will the acrobat and basketball be at the same horizontal position? (c) Find the value of h for which the acrobat will catch the ball. Assume that she and the ball must be at the same height for her to catch it.

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A circus acrobat is launched by a catapult at a speed of 15.0 [m] at an angle of 0 = 40.0° above the horizontal as shown. At a distance of 20.0 [m] away, her partner is standing on a platform at a height of h meters. At the instant that the acrobat is launched, her partner throws a basketball towards her horizontally at a speed of 5.00 [m/s]. Ignore air resistance in solving this problem. -20 m y A 5 m/s 15 m/s origin (a) Write equations for the horizontal and vertical positions as functions of time for both the acrobat and the basketball. Use the coordinate system prescribed in the diagram. (b) When will the acrobat and basketball be at the same horizontal position? (c) Find the value of h for which the acrobat will catch the ball. Assume that she and the ball must be at the same height for her to catch it.
Transcribed Image Text:A circus acrobat is launched by a catapult at a speed of 15.0 [m] at an angle of 0 = 40.0° above the horizontal as shown. At a distance of 20.0 [m] away, her partner is standing on a platform at a height of h meters. At the instant that the acrobat is launched, her partner throws a basketball towards her horizontally at a speed of 5.00 [m/s]. Ignore air resistance in solving this problem. -20 m y A 5 m/s 15 m/s origin (a) Write equations for the horizontal and vertical positions as functions of time for both the acrobat and the basketball. Use the coordinate system prescribed in the diagram. (b) When will the acrobat and basketball be at the same horizontal position? (c) Find the value of h for which the acrobat will catch the ball. Assume that she and the ball must be at the same height for her to catch it.
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