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You are watching a friend practice archery when he misses the target completely, and the arrow sticks into the ground. Discouraged, your friend asks whether you can help by estimating the speed with which the arrow left the bow. Remembering your physics class, you realize that you can do so by measuring its height above the ground when it was launched, if you assume the arrow was launched horizontally and that the ground is level. For your analysis, you let h represent the arrow’s height above the ground when it was launched, v0 represent the launch speed, and θ represent the angle the arrow makes with the horizontal when it is stuck into the ground. Find an expression for v0 in terms of h and θ.
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Physics for Scientists and Engineers: Foundations and Connections
- v sin 20 gives the distance x travelled (in feet) by a projectile launched from 32 The formula r% = the ground, with initial velocity v (in feet/sec) and initial angle 0 (in radians or degrees). a. Write an expression for the total differential in x. b. Use the total differential to estimate the error in calculating the range of a projectile with initial velocityv 100 ft/sec and initial angle 0= 50 degrees, with measurement errors of dv = t10 ft/sec (for velocity) and d6==5 degrees (for the initial angle). (Note: remember to use radians for the differential in 0.)arrow_forwardWhile vacationing in the prairie you go on a nature walk. First you walk 160 m south, then a coyote chases you 260 m southwest, then you walk 300 m in a direction 40° east of north. First draw an accurate graphical representation of your motion using a ruler and a protractor. Then use either trigonometry or components to find the displacement (in m) that will return you to your starting point by the most direct route.arrow_forwardThe path of a volleyball thrown over a net is modeled with the function A(x)=-0.02x^2 + 0.6 + 5,where x is the horizontal distance ,in feet,from the starting point,and A is the altitude of the ball in feet. Write an equation that can be solved to find out how far the ball travels horizontally before it hits the ground. Then find the distance rounded to the nearest foot. Equation: distance:arrow_forward
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- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning