3) A golf ball is hit at a cliff 150m away with an initial velocity of 70m/s at angle of 40° to the horizontal. a) How long will it take for the ball to hit the cliff? b) At what height did the ball strike the cliff?

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We have a projectile motion problem. A golf ball is hit toward a cliff 150 meters away with an initial velocity of 70 meters per second at a 40-degree angle to the horizontal. We need to find how long it takes to hit the cliff and at what height it strikes. To find the time it takes for the ball to hit the cliff, we need to analyze the horizontal motion. First, we calculate the horizontal component of the initial velocity using cosine of 40 degrees. This gives us 53.62 meters per second. Then we use the horizontal motion equation: distance equals horizontal velocity times time. Solving for time, we get 150 meters divided by 53.62 meters per second, which equals 2.80 seconds. Now we find the height at which the ball strikes the cliff. First, we calculate the vertical component of initial velocity using sine of 40 degrees, which gives us 44.996 meters per second. Then we use the vertical motion equation that includes gravity. Substituting our time of 2.80 seconds, we get 125.86 meters minus 38.33 meters due to gravity, resulting in a height of 87.5 meters. Let's watch the complete trajectory of the golf ball. The ball follows a parabolic path due to gravity. We can see the time and height changing as the ball travels. At exactly 2.80 seconds, the ball reaches the cliff at a height of 87.5 meters. This completes our projectile motion analysis with the final answers: time to hit cliff is 2.80 seconds, and height at impact is 87.5 meters.